Like \ell but for j

The boondoxo calligraphics seem to fit the bill.

\documentclass{article}
\usepackage{amsmath}
\usepackage[cal=boondoxo]{mathalpha}

\newcommand\jay{\mathcal{j}}

\begin{document}
\[ \jay ( i \to j ) \]
\end{document}

You edited your answer to mention that you had found the STIX fonts. This has a similar style, but I personally prefer this less-slanted version.

You could also load this alphabet as \usepackage[scr=boondoxo]{mathalpha} and use it as \mathscr{j}, leaving \mathcal untouched.

While you ask about PDFTeX-compatible packages, anyone using unicode-math can get a very similar \mathscr alphabet with the command

\setmathfont{STIX Two Math}[
  range={scr,bfscr},
  Scale=MatchUppercase,
  StylisticSet=1 ]

If you need to use three different mathematical script alphabets in the same paper, yet you must use a legacy engine that limits you to sixteen 8-bit math alphabets, you might adapt the relevant commands from BOONDOX-uprscr.sty and uboondoxuprscr.fd and reconsider some of your choices in life.

\documentclass{article}
\usepackage{amsmath}

\DeclareFontFamily{U}{boondoxuprscr}{\skewchar \font =45}
\DeclareFontShape{U}{boondoxuprscr}{m}{n}{
    <-> BOONDOXUprScr-Regular}{}
\DeclareFontShape{U}{boondoxuprscr}{b}{n}{
    <-> BOONDOXUprScr-Bold}{}

\DeclareMathAlphabet{\mathboondoxo}{U}{boondoxuprscr}{m}{n}
\SetMathAlphabet{\mathboondoxo}{bold}{U}{boondoxuprscr}{b}{n}

\newcommand\jay{\mathboondoxo{j}}

\begin{document}
\[ \jay ( i \to j ) \]
\end{document}

You can also get this one symbol without using up one of your limited math alphabets.

\documentclass{article}
\usepackage{amsmath}

\DeclareFontFamily{U}{boondoxuprscr}{\skewchar \font =45}
\DeclareFontShape{U}{boondoxuprscr}{m}{n}{
    <-> BOONDOXUprScr-Regular}{}
\DeclareFontShape{U}{boondoxuprscr}{b}{n}{
    <-> BOONDOXUprScr-Bold}{}

\newcommand\jay{\text{\fontencoding{U}\fontfamily{boondoxuprscr}\fontshape{n}\selectfont j}}

\begin{document}
\[ \jay ( i \to j ) \]
\end{document}

This implementation does not support \boldsymbol{\jay}, but will use the bold version if the surrounding text is bold. It assumes you will be setting \bfseries\boldmath at the same time. To always use the medium weight, add \fontseries{m} before \selectfont.

You can try also MathTime Professional 2 Fonts where the "complete" version provides a complete math typesetting environment.

\documentclass[12pt]{article}
\usepackage{newtxtext}
\usepackage[mtpccal]{mtpro2}
\begin{document}
$\mathcal{j}(i\to j)$ and $\mathcal{l}(i\to j)$ (comparated with $\ell(i\to j)$)
\end{document}