Aasimar can be found in the Monster Volo Guide and the relevant part of their description is below:
Aasimar carries in their souls the light of the heavens. They descend from humans with a touch of the power of Mount Celestia, the divine kingdom of many legitimate deities. Aasimar were born to serve as champions of the gods, their birth hailed as a blessed event.
The description is "champions of the gods", gods in general without specific reference to a particular deity. The only indication given to us is that Mount Celestia is home mainly to good deities. The following section also assumes:
Aasimar are placed in the world to serve as guardians of the law and good. Their clients expect that they will attack the evil, give the example and reinforce the cause of justice.
Thus, although all this is only a descriptive text, the assumption is that most Aasimar will follow a good legal deity. This should not be the case however, the description continues by mentioning their conflicting souls:
Despite his celestial origin, aasimar is mortal and has free will. Most aasimar follow their orderly path, but some believe that their abilities are a curse. These discontented aasimar are generally content to turn away from the world, but some become agents of evil. In their minds, their exposure to heavenly powers was nothing more than brainwashing.
Remember however that it is only advice and that there are no restrictions regarding the alignment, divinity or class of breeds in the 5th edition. What gods exist in your world depends on your DM and you can work with them to decide which one is best for your character. If you choose to be an archetypal aasimar, it would probably be a good, legitimate god, but you do not have to follow that.