1. Traditional Arabic script:
حیدری
2. Persian script:
حيدرى
The main difference lies in the use of the "ی" (y) at the end of the name. The traditional Arabic script uses a "ی" with two dots above, while the Persian script uses a "ی" with a single dot above.
Both ways are acceptable and understood by native Farsi speakers. It really comes down to personal preference.