Can I claim my new home construction for my 2024 taxes?

No.  A personal residence even if newly built is not a tax deduction.

If you are asking about itemizing and claiming the interest, then yes, if you are itemizing and you were building your house in 2024, you can claim the interest on the mortgage. In order to benefit from the mortgage interest your total itemized deductions would need to be more than your standard deduction. 

Itemized expenses include mortgage interest, gambling losses up to winnings,  charitable contributions, state and local taxes up to $10,000, medical expenses in excess of 7.5% of your AGI and casualty and losses in excess of 10% of you AGI with the first $100 not counting towards the loss.  

The 2024 Standard Deductions are as follows:

• Married Filing Joint (MFJ)              $29,200
• Married Filing Separate (MFS)      $14,600
• Head of Household (HOH)             $21,900 
• Single                                                 $14,600                                

Blind or over 65 and MFJ or MFS add $1,550

Single or HOH if blind or over 65 add $1,950

Standard versus Itemized Deduction