for a specified student can i be 20 or is it only 24

What do you mean by "Specified student"

A student can be any age for an education credit. 

A student needs to be under the age of 24 to be claimed as a dependent by someone else, (so yes, 20 would count)

Does this answer your question or are you asking something else? 

There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" [QR] 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 himself.

If you don't meet the rules for being a QC dependent, then you must have less than $5050 of income to be a QR dependent. See full dependent rules at:

https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Return/INF12139.html

The support test is different for each type. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.