Which authentication method to use in this situation

I created 2 Web APIs for payment transactions one of them to take data from database and to insert confirmation to database, the other one to deal with external company and take this data from the first api and send it to epayment company to collect money from clients but I don’t know which authentication method to use for the first and second APIs someone advice me to use basic authentication for the first api and JWT for the second one but i want your opinion

Also I need to know which one is better to use in this situation JWT or oauth2 ?

Should i discuss this with that payment company which authentication method to use or they have nothing to do with it and this will not affect on them ?