Purity: Invalid Tayammum Due to Mistaken Belief
Practical Laws of Islam as per the teachings of Ayatullah Sistani
Ruling 682:
If someone is certain that performing tayammum with a particular thing is valid and he does so, and afterwards he realises that performing tayammum with that thing is invalid, he must perform the prayers he had performed with that tayammum again.
-Ayatullah Sistani, Practical Laws of Islam, Purification (Taharah)