I would be very sceptical with such claims, especially when you met her in a bar when you were on holiday in Thailand. For Thai (bar) girls claiming they are pregnant is one of the top 10 scams in Thailand. The girl will say she is pregnant but she is not and it is just a trick to ask you for more money and to milk you as much possible even after the relationship has ended and you are back home. She will ask money for an abortion or money to raise the baby or for any other pupose for which you are willing to pay. Funny thing is that this trick is often played with several foreigners at the same time.
Legal rights and responsibilities between a man and a child primarily exists based on Thailand civil laws, section family law, see reference links below.