How to produce the symbol ȶ in pdfLaTeX?

A bit of a fusion of the previous two answers, which declares either Unicode characters for use with PDFLaTeX or tipa-compatible commands for use with LuaLaTeX or XeLaTeX:

documentclass{article}
tracinglostchars=2
usepackage{iftex}

pagestyle{empty} % format this MWE for TeX.SX
usepackage[paperwidth=10cm]{geometry}

iftutex
  usepackage{fontspec}
  setmainfont{Charis SIL}
  DeclareTextSymbol{textctt}{UnicodeEncodingName}{"0236}
  DeclareUnicodeAccent{textsubbar}{UnicodeEncodingName}{"0331}
else
  usepackage[T3,T1]{fontenc}
  usepackage[noenc,safe]{tipa}
  usepackage{XCharter}
  usepackage{substitutefont}
  
  substitutefont{T3}{rmdefault}{ptm}
  substitutefont{T3}{sfdefault}{phv}
  substitutefont{T3}{ttdefault}{cmtt}
  DeclareUnicodeCharacter{0236}{textctt}
  DeclareUnicodeCharacter{1E6F}{textsubbar{t}}
  DeclareUnicodeCharacter{02B2}{textsuperscript{j}}
fi

begin{document}

Some linguists use ȶ to represent a sound in Korean whose IPA symbol is ṯʲ.

Some linguists use {textctt} to represent a sound in Korean whose IPA symbol
is textsubbar{t}textsuperscript{j}.

end{document}

As the only tipa-encoded fonts are the Computer Modern family, Times, and Helvetica, this template selects Times as the IPA serif font, Helvetica as the IPA sans-serif font and Computer Modern Typewriter as the IPA monospace font.

One disadvantage is that combining characters do not work in PDFTeX, due to engine limitations that Frank Mittelbach has said “cannot be realistically overcome.” You must use precomposed characters with PDFTeX.

A more flexible version might check iffontchar to see whether the current font has a given symbol, and if not, fall back to one that does. Or it might declare them the way the LaTeX kernel integrated textcomp, with DeclareTextCommand and DeclareTextAccent for both Unicode and the T3 encoding.

See Sergio's answer if you can use a modern Unicode engine like LuaLaTeX (or XeLaTeX).

If you want to access the symbol in pdfLaTeX, it helps to know that this is an obsolete IPA symbol, so you can use the tipa package: It provides the symbol as textctt (standing for text curly tail t):

documentclass{article}
usepackage[safe]{tipa}
begin{document}
textctt
end{document}

Also a general hint if you don't find symbols using detexify: There is a similar site https://shapecatcher.com/ which searches all Unicode symbols.

It is the Unicode Character 'LATIN SMALL LETTER T WITH CURL' (U+0236), see https://www.fileformat.info/info/unicode/char/0236/index.htm

If you use XeLaTeX and STIX Two fonts (see https://ctan.mirror.garr.it/mirrors/CTAN/fonts/stix2-otf/StixTwoMath.pdf, page 8), you can get that character by inserting the unicode code/name in the way your editor accepts it.

In Emacs, "Alt+X insert-char [Enter]", then "0236" (without quotes.)