Hello, I applied for a tax refund in April, my federal tax was credited to my account but my state tax was not. I've been waiting for a long time but no change

Call an agent from your state department of revenue for the status of the state tax refund.

See this TurboTax support FAQ for state contacts - https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/contact-state-department-revenue/L9qVToi02_US_en_US

I think I misunderstood, sorry my state tax was paid but my federal tax was not paid

Same answer ... different taxing agency ...

If accepted by the IRS use the federal tax refund website to check the refund status - https://www.irs.gov/refunds