There is no official word from Yahoo that they charge a fee for recovering your account. In fact, most sources say you can retrieve your account for free using their self-service options 

Here's the official Yahoo account recovery page:  Yahoo Account Recovery Cost

There might be some situations where a fee comes into play:

Complex recovery: If your situation is particularly complicated, like multiple failed attempts or a compromised account, Yahoo might offer premium recovery with a fee. 

The exact cost isn't advertised, but some sources suggest around $19.99.

Customer Support: While contacting Yahoo support itself shouldn't incur a cost, if their help requires extra effort on their end, there's a chance of a fee being involved.

To avoid any fees, try the free account recovery options first and keep your account information up to date.