Tristan Thompson is trying to keep a tightly-sealed lid on info from his latest paternity case -- asking a judge to silence the woman who claims she's carrying his child from leaking info about the case ... while he continues to blast her as being out for fortune and fame.

The NBA star filed an emergency petition Tuesday in Harris County, TX -- asking the judge to issue a gag order in the case ... barring the parties (himself and Maralee Nichols) from speaking out about the case as it plays out in court.

Tristan points to multiple instances in which he believes Maralee has violated what he claims is a confidentiality order the judge orally granted earlier in the case after she sued him over paternity.