Fill with @row_number based on group field in QGIS 3

Do you need to use a field calculator? If not, the "Add autoincremental field" algorithm from the processing toolbox does what you want including the grouping.

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References:

• How to Add Auto Increment Field in QGIS

If you know the row number of the beginning of each group, you can create a group_row_number field in the Field Calculator with a simple case when statement.

In my example, I have groups A, B, C and D. Group A is rows 1-4. Group B is rows 5-8. Group C is rows 9-12. Group D is rows 13-17.

Field Calculator expression:

Result:

The generalized formula is:

case
  when "groupfieldname" = 'first group name' then @row_number
  when "groupfieldname" = 'second group name' then @row_number - [final_row_number_of_first_group]
  when "groupfieldname" = 'third group name' then @row_number - [final_row_number_of_second_group]
  ...
end

Credits to @Gabriel De Luca from his answer https://gis.stackexchange.com/a/364575/99589

In the Field Calculator use the following expression array_find(array_agg($id,"group"),$id)+1, where "group" is an attribute that will restart the count when a new group appears.