Valmiki Ramayan does not show that Sita possessed any Siddhis/riddhis. However, she is shown to have followed her dharma without fail, and she pray to Agni to protect Hanuman when she learnt that his tail was set on fire. She also issues the below prayer to Hanuman in Sundara Kaand -
tvam asmin kaarya niryoge pramaaNam hair sattama
hanuman yatnamaasthaaya dukha kshaya karo bhavaa!
Meaning: You are the living-proof of an acheiver of all desired acts, please destroy this sorrow of mine, o Hanuman!
There are 3 individuals in Valmiki Ramayan, who do 'Jai' 'Jai's to Hanuman, Sri Ram in Kishkinda Kaand, with Lakshman also by his side and then Sita in Sundara Kaanda. Hence you have the Hindi verse used in Bhajanas -
Raam Lakshman Jaanaki
Jai bole Hanumaan ki!!