Short answer: If you have taken pachchakkhān / niyam of “no green vegetables (shaak/saag)” in Paryushan, then karasuri/kasuri methi should not be eaten.

Reason in simple words:

• Kasuri methi is basically methi leaves (a green leafy vegetable), only dried.
• In Paryushan, most Shwetambar and many Digambar Jains avoid all green leafy vegetables, including methi, palak, coriander, etc., to reduce hiṁsā in Chaturmās. ( jainknowledge.com)

So:

• If your family / sangh niyam is: “no green vegetables” → don’t eat kasuri methi.
• If someone has taken only “no root vegetables” (and their guru/sangh clearly allows some above‑ground vegetables and dried leafy masala), then it depends on that local maryadā – but traditionally, methi (even dried) is kept avoided in Paryushan to be on the safer, more saiyam side.

Best is to follow:

1. Whatever pachchakkhān you have already spoken.
2. Guidance of your guru / local sangh maryadā.

For a simple list of what is and isn’t eaten in Paryushan, you can refer here: Food rules in Paryushan