Is a married man with two children who supports his mother eligible for zakat, given that he has car debts and a loan, and only a quarter or less of his salary remains?

It is permissible for you to take from zakat if your income is insufficient for your basic needs and those you support, as you would then be considered among the needy (masakeen) or the poor (fuqara'). It is also permissible for you to take from it if you have permissible debts that you cannot repay, in which case you would be among the debtors (gharimeen). However, if these descriptions do not apply to you, then it is not permissible for you to take from zakat.