Please check your bill again and post a new, separate question. The US stopped issuing fractional (less than $1) bills in the 19th century and no bills are dated 1944. It may be a military payment certificate or a bill issued for use in combat zones, in which case there should be some indication of that on the bill.
There is no 1944 liberty dollar. There is a 1944 liberty walking half dollar. The average value of these is about 10-12 dollars.
Please post a new question with the bill's country of origin. Neither the U.S. nor Canada, the major dollar-using countries in 1944, issued half-dollar notes at that time - just coins.
The 1944-S Walking Liberty half dollar is a common coin, most show heavy wear and have a average retail value of $12.00. Better grade can be $15.00 to $25.00. Mint State coins are $30.00 to $50.00 or more.
Please check your coin again. JFK was just a young naval officer in 1944. The first half dollars with his portrait were issued in 1964, after his assassination.
The '44-D half dollar is a fairly common coin. It's worth around $11 in average condition and closer to $30 if uncirculated.
Average circulated Walking Liberty half dollars from 1940 to 1947 regardless of Mintmarks are valued at $14.00.
a half hundred dollar bill is worth $50
There are twenty half dollars in a ten dollar bill.
It is worth half a cent.
So many were made that if it shows any wear the value is for the silver, about $10.00. Only a Mint State coin has more value.
The coin is a very common date " War Years" Walking Liberty half, unless it's a super high grade coin the value is just for the silver, about $10.00
If there is at least 51% of the bill, it can be taken to a bank in exchange for a replacement note of equal value.