The county clerk's office in SOME counties will do a courtesy search, but if it takes more than a few minutes they will usually tell you to get an attorney which they just happen to have the name of handy, if you get my drift. Whoever does it will charge you by the hour most likely. It is expensive and may not be worth it. The best thing in my humble opinion is to send a "Statement of Claim" to the county where your minerals are, addressed to County Clerk. This puts your name and the minerals you own where they can be found by landmen. If they want to lease your minerals they will do the search before contacting you. Saves you a lot of money and time. If you don't have a Statement of Claim", stop by a mineral leasing office and pick one up, make plenty of copies (it's a one page document) and start sending them out and wait. If you have more money than patience have a landman do the research for you. Simple as that.
I wish you lots of luck with them.