Santa Claus is a mythical representation of Nikolaos of Myra ("Saint Nicholas"), a Greek bishop born in the Roman Empire of what is now modern day Turkey. Santa appears in the Teenage Mutant Ninja Turtles Magazine story "Twas the Night Before Christmas", where he is held up at gunpoint by Bebop and Rocksteady as he is delivering presents. The Ninja Turtles arrive to stop the two mutants, and Santa ends up giving all six of them gifts, saying that Christmas should be about peace and goodwill, before taking his leave.
In other media
Characters in other incarnations of the Teenage Mutant Ninja Turtles franchise have dressed up as Santa Claus for Christmas, including Michelangelo in "The Christmas Aliens" of both the Mirage continuity, Hamato Splinter in "The Christmas Aliens" of the 2003 TV series, and Splinter in issue #89 of the IDW continuity.