Why there is a red color in right side?
Getting colour to work naturally in tex is really tricky.... Here I would just simply force it back to black with
\jverse{9}\textcolor{black}{Jesus said to him,} \textcolor{red}{``Have I been...
If using lualatex is a possibility then you could use luacolor package which keeps the same color or xcolor commands that you are used to but uses a completely different machanism to internally record colours that acts far more like font changes and so splitting boxes does not cause colour to leak in the way that happens with the classic tex colour mechanisms.
For the example here this gives black for the first phrase in each column as intended:
I just made two changes, removing the fontenc package and adding the luacolor package. No changes in the actual document text.
\documentclass[twoside,letterpaper,11pt]{book}
\usepackage[margin=1.5cm]{geometry}
% not for luatex \usepackage[T1]{fontenc}
\usepackage[usenames,dvipsnames,svgnames,table]{xcolor}
\usepackage{luacolor}% load after xcolor
%\usepackage[english]{babel} %% This package make sure for hyphenation problem
\usepackage{ebgaramond}
\usepackage{lipsum}
\usepackage{parallel,graphicx}
\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhf{}
\fancyhead[RO,LE]{\rightmark}
% \fancyhead[RO,LE]{\leftmark} %% display chapter in header
\renewcommand{\headrulewidth}{.5pt}
\fancyhead[LO,RE]{\thepage} %% To display numbering on every page alternately left and right
% \fancyhead[LO]{\small\thetitle} % Odd page header and number to right top
% \fancyhead[RE]{\small\thetitle} % Even page header and number at left top
\setlength{\headwidth}{\textwidth}
\setlength{\headheight}{15pt}
\setlength{\headsep}{0pt}
\setlength{\columnseprule}{0pt}
\usepackage[colorlinks]{hyperref}
\newcommand{\jChapter}[1]{\noindent\scalebox{2.5}{\color{red}\textbf{#1}\hspace{0.3mm}}}
\newcommand{\jverse}[1]{\noindent\textcolor{cyan}{\scalebox{1.0}{\textbf{#1\hspace{1.0mm}}}}}
%% Starts Add
%\newcommand{\story}[1]{\hfill\large\it\textbf{#1}\hfill~}
\newcommand{\story}[1]{\vspace*{2mm}\centering\it\textbf{#1}}
%%%% End Add
\makeatletter
\newcommand\versenumcolor{red}
\newcommand\chapnumcolor{red}
\renewcommand\paragraph{%
\@startsection{paragraph}{4}{\z@}%
{.25ex \@plus.25ex \@minus.1ex}%
{-.5em}%
{\normalfont\normalsize\bfseries\color{\versenumcolor}}}%
\newlength{\biblechapskip}
\setlength{\biblechapskip}{1em plus .33em minus .2em}
\newcounter{biblechapter}
\newcounter{bibleverse}[biblechapter]
\renewcommand\chaptername{Book}
\let\ltx@chapter=\chapter
\let\ltx@paragraph=\paragraph
\newcommand{\book}[1]{%
\gdef\currbook{#1}
\ltx@chapter{#1}}
\newcount\biblechap@svdopt
\newenvironment{biblechapter}[1][\thebiblechapter]
{\biblechap@svdopt=#1
\ifnum\c@biblechapter=\biblechap@svdopt\else
\advance\biblechap@svdopt by -1\fi
\setcounter{biblechapter}{\the\biblechap@svdopt}
\refstepcounter{biblechapter}
\lettrine{\color{\chapnumcolor}\lower-6pt\hbox{\thebiblechapter}}{}\ignorespaces}
{\vspace{\biblechapskip}}
\renewcommand{\verse}[1][\thebibleverse]{%
\refstepcounter{bibleverse}
\markright{{\scshape\currbook} \thebiblechapter:\thebibleverse}
\ifnum\c@bibleverse=1\else
\ltx@paragraph*{#1}\fi}%
\makeatother
\title{Translation}
\date{}
\author{}
\usepackage{lipsum}
\usepackage{ragged2e}
\newcommand{\BookLine}{ \centering\noindent\rule{19cm}{1pt}}
\newcommand{\BookNote}[1]{{\begin{center} \textbf{KEPACHINI} \justify
#1
\end{center}
\BookLine
\vspace{2mm}
}}
\usepackage[perpage]{footmisc} %%% To restart footnote numbering on every new pages
\begin{document}
\renewcommand{\thefootnote}{\emph{\alph{footnote}}}
\frontmatter
\maketitle
\tableofcontents
\mainmatter
\setlength{\columnseprule}{.5pt}
\begin{Parallel}{9.0cm}{9.0cm}
\ParallelLText{\jverse{9}Jisu thakddunsi pulo, \textcolor{red}{``Philip, ne lapu-an arni keding nangtum along nangkedodun anta nangtum nephan nechininelangma? Nephan nekethek-long abang ke Po aphanta thek-long-lo. Tangte nang kopisi, `Netum aphan Po nepaklangtha,' pu kepulangma?}}
\ParallelRText{\jverse{9}Jesus said to him, \textcolor{red}{``Have I been with you all this time, Philip, and you still do not know me? Whoever has seen me has seen the Father. How can you say, `Show us the Father'?}}
\ParallelPar
\end{Parallel}
\end{document}
An alternative to David Carlisle’s excellent answer is to switch from obsolete 8-bit encodings to fontspec and use its Color option. That allows you to use Unicode, and any standard font you could use in your word processor.
You could in fact combine this with his answer, by adding the luacolor package.
Setting the Color= option on a font isn’t compatible with \textcolor from xcolor, so you also have to update the other commands that change color to use \addfontfeatures.
I also took the liberty of adding \usepackage{microtype}. If you compile with LuaLaTeX, its font expansion should cut down drastically on the problems you seem to be having with hyphenation and word-wrapping.
\documentclass[twoside,letterpaper,11pt]{book}
\usepackage[margin=1.5cm]{geometry}
\usepackage[usenames,dvipsnames,svgnames,table]{xcolor}
\usepackage{parallel,graphicx, fontspec, microtype}
\usepackage[oldstyle]{ebgaramond}
\usepackage[colorlinks, unicode]{hyperref}
\newcommand{\jChapter}[1]{\noindent\scalebox{2.5}{\addfontfeature{Color=red}\textbf{#1}\hspace{0.3mm}}}
\newcommand{\jverse}[1]{\noindent\scalebox{1.0}{\addfontfeature{Color=cyan}\textbf{#1\hspace{1.0mm}}}}
\newcommand\redletter{\addfontfeature{Color=red}}
\DeclareTextFontCommand\textred{\redletter}
\newcommand\uncolor{\addfontfeature{Color=black}}
\DeclareTextFontCommand\textblack{\uncolor}
\begin{document}
\begin{Parallel}{9.0cm}{9.0cm}
\ParallelLText{\jverse{9}Jisu thakddunsi pulo, \textred{``Philip, ne lapu-an arni keding nangtum along nangkedodun anta nangtum nephan nechininelangma? Nephan nekethek-long abang ke Po aphanta thek-long-lo. Tangte nang kopisi, `Netum aphan Po nepaklangtha,' pu kepulangma?}}
\ParallelRText{\jverse{9}Jesus said to him, \textred{``Have I been with you all this time, Philip, and you still do not know me? Whoever has seen me has seen the Father. How can you say, `Show us the Father'?}}
\ParallelPar
\end{Parallel}
\end{document}
This adds the new commands, \redlettter Text in red, \textred{Text in red}. This would require changes to your source, but at least it would make it trivial to change the red-letter text to another style or shade if you ever wish to.
If a search-and-replace for \textcolor is infeasible, you could also (although I don't recommend it) change the meaning of \textcolor with \renewcommand.
It turns out there’s an even simpler answer. Heiko Oberdiek wrote a package pdfcolparallel that fixes this very bug in parallel using color stacks. (Arguably, this should’ve been resolved by replacing the buggy package that has been abandoned since 2003, not by adding a second one with a different name.)
Like before, I compiled with LuaLaTeX, removed the fontenc package because ebgaramond on LuaLaTeX loads the more-modern OpenType version, and added microtype to improve the hyphenation on the left column.
\documentclass[twoside,letterpaper,11pt]{book}
\usepackage[margin=1.5cm]{geometry}
\usepackage[usenames,dvipsnames,svgnames,table]{xcolor}
\usepackage{pdfcolparallel, graphicx, microtype}
\usepackage[oldstyle]{ebgaramond}
\usepackage[colorlinks, unicode]{hyperref}
\newcommand{\jverse}[1]{\noindent\textcolor{cyan}{\scalebox{1.0}{\textbf{#1\hspace{1.0mm}}}}}
\begin{document}
\begin{Parallel}{9.0cm}{9.0cm}
\ParallelLText{\jverse{9}Jisu thakddunsi pulo, \textcolor{red}{``Philip, ne lapu-an arni keding nangtum along nangkedodun anta nangtum nephan nechininelangma? Nephan nekethek-long abang ke Po aphanta thek-long-lo. Tangte nang kopisi, `Netum aphan Po nepaklangtha,' pu kepulangma?}}
\ParallelRText{\jverse{9}Jesus said to him, \textcolor{red}{``Have I been with you all this time, Philip, and you still do not know me? Whoever has seen me has seen the Father. How can you say, `Show us the Father'?}}
\ParallelPar
\end{Parallel}
\end{document}
You might still consider a more semantic command for red-letter text, in case, for example, you ever want to use a different shade of red. Right now, there are a lot of \textcolor{red} commands to change, and not all of them, even in your MWE, are attached to statements by Jesus in the Gospels. So you could not do a search-and-replace on them if you ever needed to change the style.
This defines \redletter Red-letter text and \textred{Red-letter text}:
\newcommand\redletter{\color{red}}
\DeclareTextFontCommand\textred{\redletter}