Can I claim a fee paid to Ontario college of trades to write for a licence? If so, how?

Yes.  They can be claimed as tuition fees.  Canada Revenue says:

Licensing examination fees  

Examination fees paid to an educational institution, professional association, provincial ministry or other similar institution, to take an occupational, trade or professional examination that is required to obtain a professional status recognized by federal or provincial statute, or to be licensed or certified as a tradesperson, to allow you to practice the profession or trade in Canada, may be eligible for the tuition tax credit. You should be provided with a receipt to substantiate your eligible exam fees. To view the information that should be contained in the receipt go to example of a receipt for licensing examination fee.

I understand that you actually can claim them, but the question is how does you one it technically with Turbotax online? Turbotax does not seem be aware of possibility of claiming the exam fees, all it offers is regular tuition fees.

I'd like to know this answer, too -- how to actually enter these professional exam fees in as tuition fees. The tuition fees section seems to want input based on T2202