Anakin and Ahsoka have a master - apprentice relationship, and Padme is Anakin's love. In fanfiction, Anakin might introduce Ahsoka to Padme. Ahsoka could be initially a bit shy or in awe of Padme. Padme, on the other hand, would be warm and welcoming. They could interact in a setting like a dinner at Anakin's place, where they share stories about their different experiences in the galaxy - Ahsoka's adventures with the clones, Padme's political battles, and Anakin's Jedi missions.
In some fanfictions, when Anakin is in a difficult situation, both Ahsoka and Padme come to his aid. Ahsoka uses her combat skills and Padme uses her influence. They might argue a bit at first about the best way to help Anakin, but then realize that they need to work together. Their interactions could show the different ways they care about Anakin and also how they can overcome their differences for a common goal.
Ahsoka could be caught in the middle of Anakin and Padme's relationship at times. For example, she might accidentally discover their secret marriage. She would be conflicted about whether to keep it a secret or tell the Jedi Council. This would lead to intense interactions between the three. Anakin would be worried about Ahsoka's decision, Padme would try to reason with Ahsoka, and Ahsoka would have to grapple with her loyalty to Anakin, the Jedi Code, and her friendship with Padme.