No, you cannot deduct the construction costs in 2020. The construction costs are capital costs.
If the construction costs were $50,000 you can depreciate $50,000 over 39 years.
You are able to deduct the operating expenses of this space if separately metered or by allocating the total property's utilities if not separately metered.
You can have the accessory building appraised separately for property taxes and insurance purposes as well.