My business is LLC, only issued one 1099 NEC for a contractor for $7600, do I have to file 940 or 944? Or any other form?

Forms 940 and 944 are filed by employers who have employees to whom they issued forms W-2.

As you only had a contractor to whom you issued form 1099-NEC, you do not have to file form 940 or 944.

Thank you so much for your answer.

1099 NEC is the only form I have to file on this situation?

You prepare a 1099NEC .  Turbo Tax also prepares the 1096 Transmittal for it.  If you use Quick Employer Forms it efiles both to the IRS.  If you prepare them on your computer you need to mail the 1096 and 1099NEC to the IRS.