Mr McGinley, 63, was shot outside a church in Newtownbutler as a wedding involving members of the travelling community, was about to get under way.
Patrick McGinley, who is believed to be the victim's nephew, was led into Omagh courthouse by two police officers with his head covered by a blanket.
He was remanded in custody until 16 March.
During the hearing he spoke only to confirm his date of birth and address that was given as Lisfarrell, Edgeworthstown, County Longford.
A detective said he believed he could connect the accused to the charges.
A defence solicitor told Omagh Magistrates Court his client went to police by arrangement and gave a very full account of "this tragic event".
A 46-year-old man has appeared in court charged with murdering Bernard McGinley in County Fermanagh on 11 February.