Is there any established invocation in the Sharia during ablution or not?

No supplication has been authentically reported from the Prophet, peace and blessings be upon him, during ablution while washing or wiping the limbs. Whatever supplications are mentioned in this regard are an innovation and have no basis. What is legislated is to say "Bismillah" at the beginning of ablution, to utter the two testimonies (Shahadatayn) after it, and to say: "O Allah, make me among those who repent and make me among those who purify themselves" after the two testimonies.