A gun was found in a car after it was stopped by police on the Dublin Road in Enniskillen on Friday, the court also heard.
Lorenc Dashi, 34, from Dublin Road, Cavan, Mariglen Hoxha, 21, and Arlind Rrapaj, 22, of no fixed abode in Dublin are each charged with having a firearm in suspicious circumstances and possession of an offensive weapon.
Mr Dashi is also accused of obstructing a police officer, driving without a licence and without insurance.
A detective constable told Enniskillen Magistrates' Court that the gun was found hidden underneath a false floor behind the passenger seat.
The court was told that two of the men had arrived in Dublin three weeks ago and claimed refugee status.
They had been given temporary leave to remain while their case was considered, but were supposed to remain in the Republic of Ireland.
A solicitor said the pair did not realise they were in Northern Ireland.
The two men did not speak English and one of the defendants had to translate the court proceedings as no Albanian interpreter was available.
No bail application was made and the three men were remanded in custody for two weeks.
Two men from Albania who have been charged with firearms offences did not realise they were in Northern Ireland, a court has been told.