Its been a month since I quit my job because I had a special issue with the company
When they where talking to me they told me that they are going to put me on suspension
And it raised a red flag on me that it would end in termination as the days go by

So I told them that I'm giving them a verbal notice of resignation and then other representative of the company accepted that resignation but before we finished talking my store manager ask me why I want to quit on the spot and she asked is it because for the reason for looking for another job?

I'm really anxious if she can say something negative to me to my prospective employer about this issue?

She can say whatever she likes...
If she causes irreparable damages(by lying) to your image and you incurr losses, then go see an attorney. Hard to prove and ehm not worth your time...

There must be a reason they put you on suspension... if you choose to give them as a reference to your next job application they are allowed to tell the truth (what you did to get a suspension)

It is always a prerogative of your previous employer to answer inquiries about your employment with them. So just pray that they will just say the truth and fair to all.

Your next employer has a right to know your previous work history.

If, for whatever reason, you were not a good employee then your last employer has a right to tell your next employer.

As has been previously stated, she can say what she wants, as long as it's true.

They may tell that you quit without notice

They can report anything true about your work history