Yes, women can do jap (mantra jaap) during periods.

Understand it this way in Jain Dharma:

1. Periods are a natural bodily process, not a sin.

Jainism mainly focuses on antarik shuddhi (inner purity) and bhav (intention) of the soul.

1. During periods, what is usually restricted is:

- Going into garbhagriha / gabharo - Touching murtis, puja samagri, scriptures - Doing dravya-puja / abhishek / ang-puja in derasar

1. But bhav-sadhana is allowed, such as:

- Navkar Mantra jaap - Other stavan / mantra jaap softly or mentally - Dhyan, prarthana, listening to pravachan, swadhyay (by listening)

1. Digambar & Shwetambar both generally:

- Avoid idol-touch and inner-sanctum entry during menstruation - Allow jap, pratikraman, dhyan at home as inner sadhana

So, you may peacefully do jaap at home during periods, keeping:

• Clean place and clothes as per your capacity
• Respect for temple maryada (no murti / gabharo touch those days)

If you want to read more on related questions (pooja, pratikraman, temple, and periods), you can see: