How is the zakat calculated for a sum of money that has reached the zakat threshold (nisab), resulting from the collection of checks throughout the Gregorian year in an Islamic bank account?

The value of checks before they are cashed is considered a debt. The hawl (zakat (definition) year) for the money you collect from cashing them is the hawl of the principal of that debt. See when your money reached the nisab (definition) (minimum threshold) and calculate its hawl from that time. If you acquired it in one period, or if some of it was generated from other parts, then it has one hawl. However, if you acquired it in varying periods and some of it was not generated from other parts, you have two options: The first: To make its hawl for all of it upon the completion of the hawl for the first nisab you owned from it. This is easier and more beneficial for the poor. The second: To make an independent hawl for each installment you acquired. The hawl here refers to the lunar year (twelve Arabian months).