sabai mitra haru lai Namaskar...
Mero asylum all the way mathi samma nai denied bhayo. Supreme court le mero case lina manena..malai deport gareko cha ki chaina thaha huna sakena ... since i didn't get any deportation letter or such info.
ahile ma tps ma chu ra reragistration pani gareko chu. in this case k ma travel document ma nepal gayera auna sakchu?? farkera auda samasya ta hudaina. pls guide me

If you have an attorney, call him/her and ask to find out. If you don't, call the immigration court, ask for your judge's clerk and you can ask him/her. Do you know if you got withholding of removal? If so, then you have removal order against you. In this case, you need to contact the government attorney to re-open your case. With joint motion, it can be re-opened. After the case is open, you can request the court to administratively close your case (again with joint motion) based on you have TPS and you cannot be deported. To make it simpler, get competent attorney with experience. After case is closed, you can travel with ap without fear at poe.

mero case asylum officer le recently deny garyo so does i am eligible to travel outside US and return back.

Yes with advance parole. You first need to close your case if it has been referred to immigration court.