If you are being asked to enter your prior year Roth IRA contributions, you must have taken a distribution from a Roth IRA in the current year. The prior year Roth IRA contributions are needed to determine whether any of your current year contribution is taxable.
If your distribution is less than your Roth IRA basis (the amount you contributed), then there will be no income tax imposed. If it is greater than your basis, then the distribution may or may not be taxable depending on other circumstances that would make it a qualified distribution (your age and how long you have had a Roth IRA account for example).
There is not really a good solution to overcome not having records showing the contributions. It is possible that your IRA custodian would have that information.
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