Whenever you take an HbA1c test it will reflect your average glucose levels of the previous three months.
If you take the test more often than three months, the test is still valid and it still reflects the average glucose of the last three months, it is just that the earliest part of these three months will overlap with the corresponding period covered by your previous hba1c test.
Similarly, if you allow more than three months to elapse between tests then the second test will not cover the whole of the period since the preceding test.
To be honest I do not always test every three months and the time between consecutive tests has in the pasts varied from 1 month when I was trying to lower my levels to six months when I was in a more of a maintainable stage.
Pavlos