I can’t find a birth for a Patrick McLaughlin on the exact date you have given in 1878. (Nearest was an illegitimate birth in Inishowen workhouse on 31.12.1877 to Mary Anne McLaughlin. No father named). Be aware that in Ireland in the 1800s most folk didn’t celebrate birthdays and often didn’t really know when they were born. If officialdom later asked for a date of birth it was common to just make one up. The normal advice is to search a few years either side of the year you have. But searching in the Moville area (Inishowen registration district) for say 1876 – 1880 gets 24 results for this name.
Patrick McLaughlin is a very common name in Donegal and without parents names it would be hard to try and identify your ancestor accurately.
I can see from trees on Ancestry that Patrick married Frances in the USA in 1902 and died in New York (no date given). Ideally you need his marriage or death certificates to get his parents names. Otherwise it may be a bit of a needle in a haystack.