Sosthenes gets a tiny shout-out at the beginning of 1 Corinthians. Like he did with Timothy, Paul claims Sosthenes as a co-author for 1 Corinthians. Paul doesn't spend as much time referring to "we" in this letter, though, so it's pretty likely that Sosthenes wasn't a huge influence on him.
Sadly, Sosthenes doesn't get any other mentions in the Bible either. No missionary journeys. No late-night sessions defending Paul's honor. He doesn't even get stoned to death. Poor Sosthenes.