Which data sets can tell me which groups of students are attending school less and by how much?

Unfortunately, no such public data set exists that tracks the attendance of students on a periodic basis. However, there are a few ways to approach this question –

1. Check if the State MIS tracks this data, or has recorded it in the past.
2. See if any non-government public data has this data. For example, ASER.
3. Run a sample survey.