Short answer:

• How many months: Jain prabandha-literature does not give a fixed/authoritative month-count for Siddharāj Jaysinh’s gestation.
• How he was born: The early Jain sources that mention him (e.g., Hemachandra, later Merutuṅga citing earlier traditions) simply record that he was the son of King Karṇa and Queen Mīṇaldevī; they do not describe any unusual or miraculous mode of birth. Folkloric tales about a “prolonged pregnancy” or a “surgical/extraordinary” birth are later regional stories and are not accepted as reliable Jain textual history. ( en.wikipedia.org , wisdomlib.org )

A little context from Jain tradition:

• Hemachandra (a Jain ācārya patronized by Siddharāj) recounts a devotional legend about Karṇa receiving a boon for a son; this explains the birth as a result of divine grace but still does not specify months or any non-standard delivery. ( en.wikipedia.org )

In sum, within authentic Jain narrative sources there is no set number of months and no special birth-method recorded for Siddharāj Jaysinh; specific claims like “12 months” or “born by cutting the mother’s belly” are later folklore, not Jain scripture. ( wisdomlib.org )