The "byf" marking indicates your P38 was actually made by Mauser. Serial numbers ran in blocks of 10000. After the number 10000 was reached the number sequence was repeated but with an "a" suffix added. Subsequently when each block of 10000 was completed the suffix incremented to the next letter, "b", "c", "d", etc. Your suffix is "p". The "43" normally would mean the pistol was made in 1943, however your serial number implies the pistol was made in January 1944, apparently with a leftover 43 dated slide.
You have not provided enough information to give an accurate opinion of value. Does it have matching serial numbers? Has it been reblued? Condition is all important when considering value. Some use the grading scale of excellent, very good, good, fair and poor. Assuming yours is "good", that is has matching serial numbers and original finish, I would speculate your's may be worth in the neighborhood of $450 to $500.
If you would like a more comprehensive opinion on value, I suggest you post your question with pictures on p38forum.com.
Best regards
Marc
$450-$550, depending on condition.
$250-$400. depending on condition and exact model
100-500 USD
50-150 usd
100-300 depending on condition and accessories.
100-1000 depending on specifics
300-500 dollars
About $500-$600 new. Used, $250-$450, depending on condition.
Dieter Marschall's book might have what you are looking for.
350 - 550 depending of condition and completness of box, manual etc.
200-600 depending on condition and EXACT model.
it is unknown at the moment but I'm still looking, i would have thought it is the Walther P99