Do 401(a) contributions count against the annual Roth IRA contribution limits?

No it does not count in any way. A 401a plan is an opt out plan from Social Security by government employees. The funds going into the 401a are those that would have gone to SS. Both the employee and the employer pay into the 401a at a rate of 6.2% each. If the employer also offered a 401k in addition to the 401a then that could effect the ability to put into a ROTH or other IRA type plan. But because the 401a is a Private retirement security plan in lew of a government retirement security plan (Social Security) then it doesn't effect your ability to put into IRAs. All State and Local government workers in Alaska do not pay into Social Security. Up here its called the State of Alaska SBS account. The State also has a 401k in addition to the 401a. Instead of putting into an IRA if you have a 401a then I would first obtain disability insurance. I have a friend who worked for the State government. Because government employees do not pay into Social Security under the 401a plan they are not eligible to receive Social Security disability if they are unable to work due to a disability. This is true even if they have enough paid in from a privious job. Once you opt out of Social Security you cant opt back in for SS disibility. If you were to have had the required 40 quarters paid into SS and also had a 401a then you can collect SS at 67 in addition to the 401a but for disibility you could not collect SS if you are covered under a 401a plan this is why the government offers those under 401a plans the ability to buy extra private disability insurance. Make sure you have the disability insurance inplace first...then do the IRA if you so desire. Dont do as my friend did and find out AFTER you become disabled what you should have done. Trust me on this.

I on no account heard of corporation matching IRA's what you're making a contribution to an IRA is your contribution as much as the decrease while you're in an corporation matching plan, your contributions are mentioned in container #12 on the W-2

401a Contribution Limits