Thank you for posting in our forum.

You can't change the behavior when clicking the "Move First" option.
Alternatively, you can prevent a specific column to be moved via the allowMoving option via the column settings:
However, that will only prevent the specific column to be moved, while all other columns can be rearranged in any order.
If you’d like to prevent any other columns from taking the first position I suggest you use the columnMoving event and cancel it in all cases when the args.targetIndex is 0. This will ensure that moving any other column to index 0 will be canceled.

Example:

$(document).delegate(".selector", "iggridcolumnmovingcolumnmoving", function (evt, args) {
    if(args.targetIndex === 0){
        return false;
    }
});

Karen Michelle Tecson said:

And also is there a way for me to remove a column in the AddMovingDropdown Component of Column Moving?

Do you mean you want to remove the option(e.g. "Move First" option) from columnMovingDialog?

Sincerely,
Motoki

You can move the column programmatically.
https://www.igniteui.com/help/iggrid-columnmoving-movingcolumnsprogrammatically

Example:
$(document).delegate("#grid", "iggridcolumnmovingcolumnmoving", function (evt, args) {
    if(args.targetIndex === 0){
        $("#grid").igGrid("moveColumn", args.columnKey, "ProductID", true, false);
        return false;
    }
});

And we have no built-in option for removing the element in "Move Columns" box.
But you can hide the specific arrows by columnSettings.

Example:
columnSettings:[{
    columnKey: "ProductID",
    allowMoving: false
}]

Also, you can apply the custom style to that box.
Example:
#grid_moving_movingDialog ul li[data-path="ProductID"]{
  display:none;
}

Please let me know if you have any questions.
Sincerely,
Motoki

When you select the "Move First" option, you can't change the behaviour.
You may also use the allowMoving option in the column settings to prohibit a specific column from being moved:
However, this will just restrict the single column from being moved; all other columns will be able to be rearranged in any order.
If you want to prevent any other columns from taking the first position, utilise the columnMoving event and cancel it whenever the args.targetIndex is 0. Moving any other column to index 0 will be cancelled as a result of this.