What is the ruling on the zakat of a sum of money found in another bank account, which its owner recently became aware of, for a year or past years?

If the money is yours and it increases without your knowledge, zakat is due on it once it reaches the nisab (minimum threshold) and a hawl (full lunar year) passes over it. Your ignorance of it does not waive the obligation of zakat. Ignorance and forgetfulness waive the sin, but they do not waive the obligation to fulfill what is commanded. Therefore, as long as the money is yours, zakat is obligatory on it from the day you acquired ownership of it, even if you were unaware of its existence.