Put the full cost of the fees into Loan Fees Paid, as an asset, just as you're thinking it would be.

Loan Fees Amortized, also on the balance sheet, will be similar to an Accumulated Depreciation account. Every time you make an amortizing entry, you'll debit Loan Fees Amortization Expense (on the income statement) and credit this Loan Fees Amortized.

Thus the original amount of the fee will remain unchanged in Loan Fees Paid. Loan Fees Amortized will slowly build up a credit balance over the 3 years.

When the loan fees cost has been fully amortized after 3 years, you'll have a credit balance in Loan Fees Amortized which exactly equals the debit in Loan Fees Paid. You can then simply clear both of those off the balance sheet with a journal entry.