Birth Certificate and Travel to Ireland

Researching Samuel Gleghorn born 1781 -1785 Inveresk with Musselburgh, Midlothian to James Cleghorn and Betty Scot/Scott. Some other sites have him born in County Antrim, but as his mother and father (if they were James and Betty) were married and died in Inveresk so I think it unlikely that he was born in County Antrim.

Samuel married Mary Jamison in 1807 in County Antrim, Northern Ireland.

Any help will be greatly appreciated.