Tapasya can be done even in today's time to an extent. For example, Sadhakas like Swami Rama (and many others like him) did Tapasya under their Guru's guidance by living in the Himalayas.
You can read about the austerities they performed in books like "Living with the Himalayan Masters".
But that being said, Tapasya (austerity) is not at all best suited for people of Kali Yuga. It was suitable for persons living in Krita Yuga (Satya Yuga).
Manu Smriti 1.86. In the Krita age the chief (virtue) is declared to be (the performance of) austerities, in the Treta (divine) knowledge, in the
Dvapara (the performance of) sacrifices, in the Kali liberality alone
"Tapah param krita yuge .... danam ekau kalau yuge" is what Manu says. Since austerity requires abstaining from food for many days and since life force in Kali Yuga depends verily on food (as per scriptures) hence its not recommended as a valid method in this age.