I recently found out the company I work for has cheated me out of 15 cents a hour for the past year and a half, when I asked why others with the same rank as me made more, I was told they made a mistake and are willing to give me the diiference for only this year and they can't go back further, Is this correct or should I be entitled to the whole difference? I normally wouldn't bother but I inquired about a raise because new position is twice as much work, and was denied and found out a coworker is getting 1.00 more p/h for same position. I would appreciate any advice. Thank You

Unless you are in a gov't job where wages are exact for each rank, or at a company where wages are exact by rank as matter of stated policy, then an employer can pay any employee what they want. Yours has offered you back pay for this year because to go back would be a bookkeeping nightmare. Ask for X hours off, whatever works out to the $300 or so they owe you for last year. If they refuse, don't press it unless you have a case, which you may not.

First people that do the same job don't make the same amount of money, They are not required to even give you any back pay ( unless this is a government job or a union job)

So personally you should feel lucky they are giving any back pay.

Example where I work, there are 6 medical techs, and all six make different pay, sometimes a few dollars a hour difference.