No, it doesn't. Getting fired isn't going to go on your permanent record and become a scarlet letter.
If a future potential employer asks you about your previous job and/or why you were fired...guess what you tell them...
"There was a scheduling conflict between school and the hours they began asking me to work."
That's it.
Getting fired or resigning in this situation won't make a bit of difference. What it will make a difference in is if you are eligible to draw unemployment benefits (Please note that I have no idea how the Canadian system works or even if you'd be eligible). In the U.S., quitting rather than being fired will usually carry with it extra difficulties when applying for unemployment benefits.





