This study is about an anticancer drug called ponatinib which is a tyrasine kinase inhibitor given with chemotherapy to children, teenagers, and young adults up to 21 years of age with Philadelphia Chromosome-Positive Acute Lymphoblastic Leukemia who have relapsed or are resistant to other treatment. The main aims of this study are to confirm the highest dose of ponatinib tablets and minitablet capsules that can be given to participants with acceptable side effects, and to evaluate if participant's leukemia achieves remission. Participants will take ponatinib tablets with chemotherapy. For participants who cannot swallow tablets, a minitablet form of the ponatinib will be provided. Participants will take ponatinib for 10 weeks in combination with chemotherapy (reinduction and consolidation blocks) and will be followed up for at least 3 years.