In MySQL, you can't use the default auto-increment feature for what you describe, a incrementing value that starts over per year.
This was a feature of the MyISAM storage engine years ago. An auto-increment that was the second column of a multi-column primary key would start counting from one for each distinct value in the first column of the PK. See the example under "MyISAM Notes" on this page: https://dev.mysql.com/doc/refman/8.0/en/example-auto-increment.html
But it's considered not a good idea to use MyISAM because it does not support ACID. In general, I would find another way of solving this task. I would not use MyISAM.
In InnoDB, there's no way the table will generate a value that is a duplicate of a value currently in the table, or even a value less than the maximum value previously generated for that table. In other words, there's no way to "fill in the gaps" using auto-increment.
You can use ALTER TABLE mytable AUTO_INCREMENT=1
to reset the counter, but the value you set it will automatically advance to the max value currently in the table + 1.
So you'll have to generate it using either another table, or else something other than the MySQL database. For example, I've seen some people use memcached, which supports an atomic "increment and return counter" operation.
Another thing to consider: If you need a row counter per year, this is actually different from using MySQL's auto-increment feature. It's not easy to use the latter as a row counter. Besides, what happens if you roll back a transaction or delete a row? You'd end up with non-consecutive RecordId values, with unexplained "gaps." It's also a fact about the auto-increment feature that it guarantees that subsequent id's will be greater, but it does not guarantee to generate all values consecutively. So you'll get gaps eventually anyway.