Can I claim an education credit if I paid middle school tuition for my daughter (dependent)?

You cannot usally  claim a federal education credit for middle school tuition. The American Opportunity Tax Credit (AOTC) and the Lifetime Learning Credit (LLC) are designed to help with the cost of higher education, such as eligible college, university, or trade school expenses.

• However, if the school is for special education and medically necessary, it may qualify as a medical expense. 
• Additionally, you can use up to $10,000 per year tax-free from a 529 plan for K-12 tuition. Some states offer additional tax benefits for using 529 plans for K-12 education.
• Some states may offer credits and deductions (reach back out with your state for additional information).

For more detailed information, you can refer to the IRS guidelines on education credits and TurboTax's education tax credits

There is no federal credit for elementary and secondary education.  Some states have such a credit or deduction. If yours is one, it will come up in the state interview. 

https://www.edchoice.org/school-choice/types-of-school-choice/how-do-k-12-education-tax-credits-deductions-work/