Should I continue studying at a Sharia institute after repenting from cheating, or should I confess and re-study diligently? And does what I did necessitate anything upon me?

If the institute stipulates that answers should not rely on a book or a person and that Quranic recitation must be from memory, then what you did by cheating and deceiving is not permissible, for the Prophet, peace and blessings be upon him, said: "Whoever cheats is not one of us."

You must repent to Allah Almighty, and retake the studies and exams correctly. It is not enough for you to stop cheating in the future; rather, you must correct the mistake and inform the institute of the truth.

However, if the institute does not stipulate memorization and does not prohibit the use of sources, then there is no blame on you for what you did. The decisive factor in this is the institute's conditions and regulations.