Cannot convert value of type 'Range<String.Index>' (aka 'Range<String.CharacterView.Index>') to expected argument type 'NSRange' (aka '_NSRange')

You can use NSString and NSRange, also you need to change this line normalNameString.mutableString.replacingCharacters(in: range, with: attributedSubString) and use this one instead normalNameString.replaceCharacters(in: nsRange, with: attributedSubString) because mutableString is NSMutableString, and replacingCharacters expect String and not NSAttributtedString

Full code (Updated for Swift5)

    let nsRange = NSString(string: name).range(of: searchText, options: String.CompareOptions.caseInsensitive)

    if nsRange.location != NSNotFound
    {
        let attributedSubString = NSAttributedString.init(string: NSString(string: name).substring(with: nsRange), attributes: [NSAttributedString.Key.font : UIFont.boldSystemFont(ofSize: 17)])
        let normalNameString = NSMutableAttributedString.init(string: name)
        normalNameString.replaceCharacters(in: nsRange, with: attributedSubString)
        cell.name.attributedText = normalNameString
    }
    else
    {
        cell.name.text = name
    }

Please do like that,

First,

extension String {

    func nsRange(from range: Range<String.Index>) -> NSRange {
        let from = range.lowerBound.samePosition(in: utf16)
        let to = range.upperBound.samePosition(in: utf16)
        return NSRange(location: utf16.distance(from: utf16.startIndex, to: from),
                       length: utf16.distance(from: from, to: to))
    }
}

after that you have one lable and string like that,

private func setAttributedLabel() {

    let lableText = UILabel()

    let strTitle = "Basic string Double tap" // your main string
    let title:NSMutableAttributedString = NSMutableAttributedString(string: strTitle)

    // give attribute to basic string
    title.addAttributes([NSForegroundColorAttributeName:UIColor.blue ,NSFontAttributeName:UIFont.boldSystemFont(ofSize: 15)], range: NSRange.init(location: 0, length: title.length))
    lableText.attributedText = title

    // give attribute to your range string
    let rangeOfString = lableText.text?.range(of: "Double tap") // this string is subString of strTitle
    title.addAttributes([NSForegroundColorAttributeName:UIColor.gray,NSFontAttributeName:UIFont.systemFont(ofSize: 15)], range: strTitle.nsRange(from: rangeOfString!))
    lableText.attributedText = title

}

I hope it will help.

You have to create NSRange instance using Range<String.index> lowerBound and UpperBound position values as below.

let searchText = "Kiran"
let name = "Kiran Jasvanee"
let idNo = "Employee Id. \("24")"

if let range = name.range(of: searchText, options: String.CompareOptions.caseInsensitive, range: nil, locale: nil)
{
    let attributedSubString = NSAttributedString.init(string: name.substring(with: range), attributes: [NSFontAttributeName : UIFont.boldSystemFont(ofSize: 17)])
    let normalNameString = NSMutableAttributedString.init(string: name)

    let startPos = name.distance(from: searchText.characters.startIndex, to: range.lowerBound)
    let nsrange = NSMakeRange(startPos, searchText.characters.count)

    normalNameString.replaceCharacters(in: nsrange, with: attributedSubString)
    labelName.attributedText = normalNameString
}
else
{
    labelName.text = name
}  

add, self.searchBar.text! instead of "Kiran" in searchtext constant and
add item.firstName ?? "" instead of "Kiran Jasvanee" in name constant according to your requirement.

I've tried it in a demo, and code I posted working fine as below. Please check.

If name = "AKiranJasvanee"

If name = "KiranJasvanee"