The two letters (NA) at the beginning indicate 1951according to Singer's site in the related link.
Google the make and model number
Your Singer Model 301A sewing machine was manufactured in 1953 at Anderson, South Carolina.
The Singer website has resources for looking up serial numbers of Singer machines. The machine you reference is a Singer model 66, manufactured between July and October 1926.
It is a 201K and was manufactured on July 17, 1956 in Clydebank Scotland.
Machines with serial numbers beginning with NA were manufactured in 1951.
It was manufactured in 1957 in Great Britain.
mine is w1643055..and mine is a Singer 319w
Singer sewing machines manufactured prior to 1900 have serial numbers consisting of numbers only. After 1900 the machine serial numbers have a single or two-letter prefix. The letters identify the year the machine was manufactured. A sewing machine bearing the serial number AI-000.001 would not exist, as Singer skipped the "AI" prefix as the "I" could be mistaken for the numeral "1". Sewing machines manufactured in 1948 bear serial numbers beginning with "AH" and "AJ", but none bear the prefix "AI".
Serial numbers G-9.726.301 to G-0.566.400 were manufactured in 1923. If the number above begins with two letters (GO) then it was manufactured "Beginning 1935".
NB062511 is a model 301A manufactured in Anderson, South Carolina in 1956.
Machines with serial numbers GA to GY were manufactured in 1935. Serial numbers beginning G - zero were manufactured in 1923.
That singer model was manufactured in 1955 according to the Singer model number guide.