genealogy. magically you can do past life regression, but genealogy would be best. true there are very little records for your father, that doesn't mean there aren't any at all. start by tracing back as far as your family knows, if you're lucky, they can give you things like hospitals family members were born at, or when they arrived in your country, from there, the government should have records, and you'll have to go to a hall of records, or a library, or museum [or where ever they may be kept] and trace it back. it's long and tiring but rewarding in my opinion. i don't think it can be traced back to Celtic practitioners. but if your family was Irish from before the British/Romans came, then they were most likely Celtic since that was the major religion.
however, if you want to trace back to see if you're from a long line of witches and therefore are a powerful sorcerer, it doesn't work that way. it's neat, but it comes from within, lineage doesn't matter too much when it comes to magic.