Yeah, University of Alabama at Birmingham does provide scholarships based on merit. Here are some of them:

Presidential Recognition
Total Worth: Tuition and fees
Eligibility: Tuition and fees
Minimum Criteria: 30-36 ACT, 3.5 GPA
Separate application needed: No

Blazer Elite Scholarship
Total Worth: $15,000
Eligibility: $15,000
Minimum Criteria: 30-36 ACT or 1360-1600 SAT, 3.5 GPA
Separate application needed: No

Blazer Gold Schoalrship
Total Worth: $10,000
Eligibility: $10,000
Minimum Criteria: 26-29 ACT or 1230-1350 SAT, 3.5 GPA
Separate application needed: No

University of Alabama at Birmingham provides aids at an average of 9923 per student meeting 56% of students need. 99% of students with need receive financial aid at an average of 5087 need-based grant. They also provide other scholarships including Aaron Lamar, Jr. Endowed Scholarship and Camille Armstrong Endowed Scholarship.