Want to check the tax credit paid by my Employer for the quarter.

1. You can check your Form 26AS online on TIN site to see if the tax paid by employer is reflected or not. For this you need to login to TIN site using your PAN. No need of employer's TAN number.
2. You can also check the challan status by using URL https://tin.tin.nsdl.com/oltas/servlet/QueryTaxpayerAjax . But this needs information like BSR code of the branch where tax was paid, date, serial number etc. I think Form 26AS is more than sufficient.

There is no need of employer's TAN to check TDS credit.

Adding to @Phani-R reply, you may also check form-26AS on following locations:

1. Form 26AS on Income tax efiling website: Needs login on this website. You may have one if you have filed return online or you may create one using your PAN details.
2. With Online banking accounts: ICICI, HDFC, Kotak, SBI and most of the others banks have link for Form 26AS in their online banking login.