OK. I asked because the term "paternity suit" is an American one. If, as I think, you are talking about an affiliation order (sometimes known as a bastardy order), taken out against your ancestor for maintenance of an illegitimate child, then you need to be looking in the local petty sessions records. Those for West Yorkshire are at the West Yorkshire Archives (
www.archives.wyjs.org.uk). They have a paid research service, but it might be quite a long (and therefore expensive) job.