Rolling over funds from a 403(b) to a Roth IRA has no bearing on the amount that you are eligible to contribute to a Roth IRA. The taxable amount of any rollover or conversion to a Roth IRA is subtracted from AGI in determining the modified AGI that is used to establish your Roth IRA contribution limit.
Also, it's unlikely that your payroll contributions are to a Roth IRA but are instead employee contributions to a Designated Roth Account in a qualified retirement plan such as a 403(b) or 401(k). If you are still working for the employer that provides the 403(b) plan from which you would take the distribution to roll over to a Roth IRA and are under age 59½, you might be prohibited from taking such a distribution. Contact the plan administrator to see if you are eligible to take such a distribution.
"Contributions" and "rollovers" are controlled by separate rules and doing one doesn't change the rules for the other.
If this is a pre-tax 403(b), then rolling to over to a Roth IRA will also be a "conversion" and you will owe regular income tax on the amount converted, but there is no penalty. If this is an after-tax 403(b) (called "Roth" but that's not really it's name) then it is a non-taxable rollover.
Agree that if you are currently employed by the sponsor of the 403(b), they probably won't let you roll over any money to a private IRA. If you have a 403(b) from a previous employer, you will be allowed to do this.
It is also important that the money be transferred directly between the plan trustees and not come to you in the form of a check. That has the potential to cause all kinds of trouble.
And you probably aren't making payroll contributions to a "Roth IRA." You are probably making payroll contributions to an employer sponsored qualified retirement plan that might be an after-tax 401(k) or 403(b), which is Roth-like but not actually an "IRA". Employer plans and private IRAs are controlled by different sections of the tax code and have very different rules on contributions and withdrawals.
This does not change the earlier answer that your ability to do a rollover or conversion and your ability to contribute are two different things and don't influence each other.