You could set up the new studio as a Business Asset and deduct the amount you spent to build it either as an Expense or Depreciate it over several years.
Additionally, you can deduct Home Office Expenses (such as mortgage interest, property tax, insurance, etc.) in proportion to the entire home, even though yours is a separate structure.
For example, if your studio is 500 square feet, and the house is 1500 square feet, you can deduct 33% of those costs that would apply.
Here's more detailed info:
https://turbotax.intuit.com/tax-tips/small-business-taxes/managing-assets/L18WqppFX
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