Explanation:

Janani Suraksha Yojana (JSY) is a safe motherhood intervention under the National Health Mission (NHM) by the Government of India. It was launched to reduce maternal and neonatal mortality by promoting institutional deliveries among poor pregnant women. The scheme provides cash assistance to pregnant women for giving birth in a health facility.

Considering the given statements:

it is a safe motherhood intervention of the State Health Departments. - inCorrect. It is an intervention under the National Health Mission

its objectives to reduce maternal and neonatal mortality among poor pregnant women - Correct.

it aims to promote institutional delivery among poor pregnant women. - Correct.

Its objective includes providing public health facilities to sick infants up to one year of age. - This is not a direct objective of JSY. JSY primarily focuses on promoting institutional deliveries to ensure the health of mothers and newborns. However, the broader National Health Mission has components to provide health facilities to infants and children.

So, out of the given statements, the first three are correct. The answer is "Two statements are correct."