Why is turbo tax stating I cannot claim my 17 and 11 year old as dependants who resident only with myself and i support fully with no assistance?

Not sure what you entered about the two children.   If you are the custodial parent you can claim both of them as dependents.  You cannot get the child tax credit for the 17 year old---you get the $500 credit for other dependents for a child older than 16.  You can get the CTC for the younger child, though, assuming you have income from working.

Make sure you have entered your child as a dependent in My Info, and that you have entered the child's Social Security number.    Careful— do not say that your child’s SSN is not valid for employment.  If your child was born in 2024 make sure you said he lived with you the whole year.  There is an oddly worded question that asks if the child paid over half their own support.  Say NO to that question.

Have you entered income from working in 2024?  If not,  you will not receive an income tax refund based on having dependent children.

  The maximum amount of the child tax credit is now $2000 per child; the refundable “additional child tax credit” amount is $1700.   In order to get that credit, you have to have income from working.  

Take the amount you earned from working.   Subtract $2500.   Multiply the rest by 15%.  That is the additional child tax credit per child that you can get—- up to the maximum of $1700 per child.   If the amount you earned from working was low, you will not get the full $1700 per child.

 If your child is older than 16 at the end of 2024, you do not get the CTC.  But you may still get the non-refundable $500 credit for other dependents instead.

https://ttlc.intuit.com/turbotax-support/en-us/help-article/taxation/child-tax-credit/L2lNhfGDl_US_en_US?uid=m68dfq2u

https://ttlc.intuit.com/turbotax-support/en-us/help-article/taxation/additional-child-tax-credit/L6xFeMFEf_US_en_US?uid=lqnuygah

https://www.irs.gov/help/ita/does-my-childdependent-qualify-for-the-child-tax-credit-or-the-credit-for-other-dependents

And for the Earned Income Credit—-

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-credits-deductions/qualifications-earned-income-credit-eic-eitc/L7w4BFP32_US_en_US?uid=m62rmz09

https://www.irs.gov/credits-deductions/individuals/earned-income-tax-credit/use-the-eitc-assistant

https://www.irs.gov/pub/irs-pdf/p596.pdf

Look at your 2024 Form 1040 to see the child-related credits you received

PREVIEW 1040

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-return/preview-turbotax-online-return-filing/L77WCkvnu_US_en_US?uid=m681fkhr

Child Tax Credit line 19

Credit for Other Dependents line 19

Earned Income Credit line 27

Additional Child Tax Credit line 28