The US didn't print any bills dated 1944. Please check again and post a new, separate question.
It's worth about a dollar, just for the silver.
Please check your bill again and post a new, separate question. The US didn't print any bills dated 1944. 1935 is the closest date for $1 silver certificates.
There is no 1944 liberty dollar. There is a 1944 liberty walking half dollar. The average value of these is about 10-12 dollars.
I assume the value is worth around US$10,000.
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
The last US silver dollars were minted in 1935. If you turn your coin over and read the denomination on the back you'll find it's a HALF dollar. Please see the Related Question for more information.
What you have is a "Walking Liberty" half dollar. 1944 is a common year and in average circulated condition they are worth about $12 for their silver content. If uncirculated it might be worth a bit more.
The gold is plating that was added later by a private company. It destroys any collector value the coin had, but as of 01/2010 it's still worth about $7-8 for its silver content.
Check that coin again. There were no US silver dollars minted that year (or decade).
Around $1.50.
No U.S. bills are dated 1944. Please check again and post a new question. Include the letter, if any, next to the date. Don't include the serial number because it doesn't help to ID a bill.