I work in Philadelphia, Pa but live in Delaware. Does Delaware division of Revenue credit the income tax paid in Philadelphia

Yes. The credit would be taken on line 10 of your residential Delaware return. Delaware will give you credit for taxes paid to the state of Pennsylvania the local taxes paid to Philadelphia cannot be included

I work in Philly why are they taken tax out for Delawear & Philly on my check I Just move to Delawear from Philly a year ago now they saying I oh the IRS on my income tex for Philly & DE...How can this be right.