If my dependent took classes at a jr college for HS dual credit can I deduct those expenses? If I paid a deposit to her 4yr college , does it count against the Hope?

Yes, taking a deduction now for her high school dual credit post-secondary education expenses may count toward the eligibility period if she were eligible and if the expenses were deducted.

The American Opportunity Tax Credit, which replaced the Hope Credit, is available for post-secondary students pursuing a degree or certification. She will be eligible for four years only.

See the student examples on page 18 of IRS 2020 Publication 570: Tax Benefits for Education:

Example 3:

During the 2019 fall semester, Larry was a high school student who took classes on a half-time basis at College X.

Larry wasn't enrolled as part of a degree program at College X because College X only admits students to a degree program if they have a high school diploma or equivalent.

Because Larry wasn't enrolled in a degree program at College X during 2019, Larry wasn't an eligible student for tax year 2019.

Example 4. The facts are the same as in Example 3. During the 2020 spring semester, Larry again attended College X but not as part of a degree program.

Larry graduated from high school in June 2020. For the 2020 fall semester, Larry enrolled as a full-time student in College X as part of a degree program, and College X awarded Larry credit for his prior coursework at College X.

Because Larry was enrolled in a degree program at College X for the 2020 fall term on at least a half-time basis, Larry is an eligible student for all of tax year 2020.

Therefore, the qualified education expenses paid for classes taken at College X during both the 2020 spring semester (during which Larry wasn't enrolled in a degree program) and the 2020 fall semester are taken into account in figuring any American opportunity credit.

For more information, see: The Lowdown on Education Tax Breaks - TurboTax Tax Tips & Videos