Can I file a lawsuit against my employer?

The plain answer to your question is yes, anybody can sue anyone else for anything, so certainly you can sue your employer. The question is whether or not any lawsuit would have merit. In New York, you are an at will employee so you can be hired, fired or mistreated for any reason or no reason. So long as your employer's adverse treatment is not motivated by an illegal reason, the treatment, while maybe not fair, is not illegal. Failing to pay overtime for hours worked over forty for non-exempt employees is another story. You must be paid overtime if you are not exempt. Further, you must be provided with a statement showing hours worked, rate of pay and taxes withheld. If your employer is not doing this, you can sue him and you would have a valid claim. Contact an attorney.