I don’t know much about Slovak geneaology.

First, you need to collect as much information as possible about your Slovak ancestors. Where they lived? When they lived? What was their religions. Approximate births of dates. When they left the country. What they did. Every bit of information counts.

Then you need to find archives that may hold information about your relatives. Archives could be spread in several cities , even 2-3 countries.

Once you find the archive, then you will not search for someone or agency who will go into archives searching for information. Usually, it cost money to search in archives. There maybe some regulations on how archive information is retrieved.