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Tekashi69 might flee the country if he's let out of jail before his extradition to Texas ... so, a judge in New York just denied his request for bail.

Tekashi and his attorneys were in court Thursday asking the judge to let him out on bail. We broke the story ... 6ix9ine was arrested Wednesday at JFK Airport on an outstanding warrant in Texas, where he allegedly choked a teenager in a mall.

The rapper pleaded for mercy, telling the judge he's learned his lesson while sitting behind bars for a day ... and added, he needs to support his mother and other family members. The judge wasn't having it and pointed out Tekashi was just in Europe ... and didn't appear to be taking the Texas case seriously.

Also, Tekashi took a plea deal in a child sex case which requires him to keep his nose clean. The judge told him that getting arrested multiple times since then hardly upholds his end of the deal.