You can fast any days of Shawal. Therefore, if you fast for example Mondays and Thursdays, this is OK.

And Allah knows best

IS IT FINE ONE CAN KEEP SHAWWAL FASTINGS BY BREAKING INTO ONE OR TWO IN THE WHOLE MONTH OF SHAWWAL OR ELSE ONE SHOULD KEEP CONTINOUSLY SIX SHAWWAL FASTINGS

Fasting | March 30, 2014 6:30 pm
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Is it permissible for the woman who has started her menses to break the fast and eat or must she refrain from eating but still make up the fast?
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Please how should a muslim lady perform her ibadah when in her monthly period especially during fasting(last ten days)?