The New York credit appears to be limited to $5000 per principal residence. However, I am not a tax attorney and you may want to have your situation reviewed by a professional. If you feel Turbotax's instructions or computations were in error, you can attempt to make a claim under the accuracy guarantee. If accepted, Turbotax will pay the interest and any penalties (you always owe your own correct tax).
https://turbotax.community.intuit.ca/community/after-you-file-questions/help/how-do-i-submit-a-claim...
This is NY tax law section 606(g-1)
https://codes.findlaw.com/ny/tax-law/tax-sect-606.html
(g-1) Solar energy system equipment credit. (1) General. An individual taxpayer shall be allowed a credit against the tax imposed by this article equal to twenty-five percent of qualified solar energy system equipment expenditures, except as provided in subparagraph (D) of paragraph two of this subsection. This credit shall not exceed three thousand seven hundred fifty dollars for qualified solar energy equipment placed in service before September first, two thousand six, and five thousand dollars for qualified solar energy equipment placed in service on or after September first, two thousand six.
(2) Qualified solar energy system equipment expenditures. (A) The term “qualified solar energy system equipment expenditures” means expenditures for:
(i) the purchase of solar energy system equipment which is installed in connection with residential property which is (I) located in this state and (II) which is used by the taxpayer as his or her principal residence at the time the solar energy system equipment is placed in service;
(ii) the lease of solar energy system equipment under a written agreement that spans at least ten years where such equipment owned by a person other than the taxpayer is installed in connection with residential property which is (I) located in this state and (II) which is used by the taxpayer as his or her principal residence at the time the solar energy system equipment is placed in service; or
(iii) the purchase of power under a written agreement that spans at least ten years whereunder the power purchased is generated by solar energy system equipment owned by a person other than the taxpayer which is installed in connection with residential property which is (I) located in this state and (II) which is used by the taxpayer as his or her principal residence at the time the solar energy system equipment is placed in service.
(B) Such qualified expenditures shall include expenditures for materials, labor costs properly allocable to on-site preparation, assembly and original installation, architectural and engineering services, and designs and plans directly related to the construction or installation of the solar energy system equipment.
(C) Such qualified expenditures for the purchase of solar energy system equipment shall not include interest or other finance charges.
(D) Such qualified expenditures for the lease of solar energy system equipment or the purchase of power under an agreement described in clauses (ii) or (iii) of subparagraph (A) of this paragraph shall include an amount equal to all payments made during the taxable year under such agreement. Provided, however, such credits shall only be allowed for fourteen years after the first taxable year in which such credit is allowed. Provided further, however, the twenty-five percent limitation in paragraph one of this subsection shall only apply to the total aggregate amount of all payments to be made pursuant to an agreement referenced in clauses (ii) or (iii) of subparagraph (A) of this paragraph, and shall not apply to individual payments made during a taxable year under such agreement except to the extent such limitation on an aggregate basis has been reached.
(3) Solar energy system equipment. The term “solar energy system equipment” shall mean an arrangement or combination of components utilizing solar radiation, which, when installed in a residence, produces energy designed to provide heating, cooling, hot water or electricity for use in such residence. Such arrangement or components shall not include equipment connected to solar energy system equipment that is a component of part or parts of a non-solar energy system or which uses any sort of recreational facility or equipment as a storage medium. Solar energy system equipment that generates electricity for use in a residence must conform to applicable requirements set forth in section sixty-six-j of the public service law . Provided, however, where solar energy system equipment is purchased and installed by a condominium management association or a cooperative housing corporation, for purposes of this subsection only, the term “ten kilowatts” in such section sixty-six-j shall be read as “fifty kilowatts.”
(4) Multiple taxpayers. Where solar energy system equipment is purchased and installed in a principal residence shared by two or more taxpayers, the amount of the credit allowable under this subsection for each such taxpayer shall be prorated according to the percentage of the total expenditure for such solar energy system equipment contributed by each taxpayer.
(5) Proportionate share. Where solar energy system equipment is purchased and installed by a condominium management association or a cooperative housing corporation, a taxpayer who is a member of the condominium management association or who is a tenant-stockholder in the cooperative housing corporation may for the purpose of this subsection claim a proportionate share of the total expense as the expenditure for the purposes of the credit attributable to his principal residence.
(6) Grants. For purposes of determining the amount of the expenditure incurred in purchasing and installing solar energy system equipment, the amount of any federal, state or local grant received by the taxpayer, which was used for the purchase and/or installation of such equipment and which was not included in the federal gross income of the taxpayer, shall not be included in the amount of such expenditures.
(7) When credit allowed. The credit provided for herein shall be allowed with respect to the taxable year, commencing after nineteen hundred ninety-seven, in which the solar energy system equipment is placed in service.
(8) Carryover of credit. If the amount of the credit, and carryovers of such credit, allowable under this subsection for any taxable year shall exceed the taxpayer's tax for such year, such excess amount may be carried over to the five taxable years next following the taxable year with respect to which the credit is allowed and may be deducted from the taxpayer's tax for such year or years.
