As George noted above, simply because your paper trail doesn't correspond with the match you've found does not in itself prove that the match is from your paternal side. But Ancestry's '3rd cousin' indicator does constitute quite a high number of centimorgans, so it's worth pursuing further along with any other significant matches. Do you have any 'shared matches' on Ancestry with this person?
I would politely ask this match (and any other significant ones) if they can upload to gedmatch and/or familytreedna, who also do a free autosomal transfer.
The most important way to progress with deciphering your DNA results is to get people to test where you know the connection. Ideally these people will be at least one degree away from you (an uncle or first cousin would be ideal; failing that even a 2nd cousin could still be helpful). Having these tests to compare will help you to place your matches.
Since you don't know who your father was, having a known person (e.g. a first cousin) on your maternal side test would be of particular help, since if a match is also related to a maternal cousin, they are almost certainly from that side and not from your unknown paternal side. Failing this, perhaps you can use your existing research to identify some people who have already tested as maternal matches. Any known relationships will potentially help you.
The process of tracing and identifying matches is quite hard work, but you will find there are many helpful people willing to share their knowledge, and perhaps even help you interpret your results.