Your question is somewhat ambiguous in the sense that it is not clear whether you are the payer or the recipient.
Regardless, 1099s are not based on a fiscal year. Rather, 1099s are based on a calendar year and must be filed by January 31st, February 28th, or March 31st (for the prior calendar year) depending on the type and filing method.
Re 1099-MISC see: https://www.irs.gov/instructions/i1099msc#idm139665633919392
