Not if the money is sitting in the account. Also, not if you have qualified distributions.
The only time you can pay tax on gains/ earnings in a Roth is if you have:
A/ nonqualified distributions (qualified distributions info listed below)
B/ earnings on excess contributions
____What Are Qualified Distributions?
A qualified distribution is any payment or distribution from your Roth IRA that meets the following requirements.
It is made after the 5-year period beginning with the first taxable year for which a contribution was made to a Roth IRA set up for your benefit, and
The payment or distribution is: