How do i claim my college student although she had a part time job last year ? how can i make sure her taxes are filed?

She can file as a single person, but she must indicate that she is claimed as a dependent.

She would file her own separate tax return. She may not need to file if she is under the filing requirement and there is no withholding to recover.

Dependents – If you can be claimed as a dependent by another taxpayer, your standard deduction for 2021 is limited to the greater of: (1) $1,100, or (2) your earned income plus $350 (but the total can't be more than the basic standard deduction for your filing status).

You can still  claim your student child as a dependent, regardless of how much money she made.

There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test.

A child of a taxpayer can still be a “Qualifying Child” (QC) dependent, regardless of his/her income, if:

1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
2. He did not provide more than 1/2 his own support. Scholarships are excluded from the support calculation
3. He lived with the parent (including temporary absences such as away at school) for more than half the year

So, it doesn't matter how much he earned. What matters is how much he spent on support. Money he put into savings does not count as support he spent on him self.

The support value of the home, provided by the parent, is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants.

The IRS has a worksheet that can be used to help with the support calculation. See: http://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf

Furthermore, there is a rule that says IF somebody else CAN claim him as a dependent, he is not allowed to claim himself. If he has sufficient income (usually more than $12,550), he can & should still file his own tax return.   In TurboTax, he indicates that somebody else can claim him as a dependent, at the personal information section.  TT will check that box on form 1040.

Even if he had less, he is allowed to file if he needs to get back income tax withholding. He cannot get back social security or Medicare tax withholding.

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You do not report his/her income on your return. If it has to be reported, at all, it goes on his own return. If your dependent child is under age 19 (or under 24 if a full time student), he or she must file a tax return for 2020 if he had any of the following:

1.          Total income (wages, salaries, taxable scholarship etc.) of more than $12,550 (2021).
2.          Unearned income (interest, dividends, capital gains, unemployment) of more than $1100.
3.          Unearned income over $350 and gross income of more than $1100
4.          Household employee income (e.g. baby sitting, lawn mowing) over $2100 ($12,400 if under age 18)
5.          Other self employment income over $432, including money on a form 1099-NEC