There comes a point in Irish ancestry research where there simply are no more records and that point is usually around the early 1800s.
I searched Roots Ireland (subscription site) for a Thomas Stevens born in the years between 1790 and 1810. There are a handful of results but to be honest, when you are unsure of his father's name there will be no substantial evidence to prove which of these, if any, is your Thomas. The records on Roots Ireland are by no means complete and there have been many records lost over time.
To be certain of the veracity of any record the very least you would need is definite Father's name and county/parish of origin.
Unfortunately I don't think you have much chance of finding anything unless more information becomes available through another source eg. death certificate which may contain more information.