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
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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
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The payment or distribution is:
Made on or after the date you reach age 59½,
Made because you are disabled (defined earlier),
Made to a beneficiary or to your estate after your death, or
One that meets the requirements listed under First home under Exceptions in chapter 1 (up to a $10,000 lifetime limit).
https://www.irs.gov/publications/p590b/ch02.html#en_US_2016_publink1000231061
