I paid a portion of my childs college tuition out of pocket. Is there a place to enter that under the expenses?

If you received Form 1098-T from that college, the tuition you paid with cash will be reported on that form, and entered when you enter that Form 1098-T.  In this case, you don't add it again because it is already in box 1 of the Form 1098-T. If you paid qualified education expenses other than tuition, there is a screen in TurboTax to enter those expenses.

If you didn't get a Form 1098-T, you still go to the Form 1098-T section to enter your tuition, and when you answer that you did not get a 1098-T, you'll be asked if you qualify for an exception.  If you do (see exceptions on screenshot, below) you will continue and be asked for the EIN of the school you attended, and then how much you paid the school.

See the IRS website at this link, Q18 through Q20 for more information.

To find the section to enter your 1098-T, click the "magnifying glass Search" icon on the top row, enter "1098t" in the search window and press return or enter, and then click on the "Jump to 1098t" link to enter your 1098-T or indicate an exception.

Here is the screenshot of the exceptions to the "no 1098-T" question: