I was late for the namaz of fajr and caught up with the second Rakat but in Tashahhud I recited only Tashahhud and not salutation with the imam, is my prayer valid or what if I sit ideally as it was my first Rakat but second for imam will my prayer be valid.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Your reciting of the Tashahhud with the Imam, then standing up to make up for the missed Rak'ah (unit of prayer) after the Imam's tasleem is correct. If that's what you did, then your prayer is valid.

Furthermore, it is obligatory for you to know the rulings of the obligatory acts like the rulings of purification, the prayer, zakat, fasting, and similar obligations.

Allah knows best.