I'm using select statements like the following:

<SELECT ID="task" name="task">
<option value=""></option>
<option value="AA">Available</option>
...
<option value="ZZ">Completed</option>
</SELECT>

The option values include most other two-position letter combinations between AA and ZZ (e.g., HY).

To choose "HY" from the resulting dropdown list that the user sees, the user has to enter an "H" and then scroll down through the list to find "HY" or continue pressing the "H" key until "HY" displays in the dropdown list box. If the user enters "H" and then enters "Y", the list jumps to "YA" instead of "HY".

Is there a way to change how the dropdown list works, so that a user can enter "HY" and have "HY" displayed?

No there isn't. Sorry.

The user can keep pressing H until the correct one is shown.