AFAIK, programs don't have to worry about which direction they write fields in DER-encoded files, because A would be the representation in little endian on everything running an x86 processor. B would be the typical way you send byte arrays across the network because the network order is big endian so in other words the hash that was created needs to be "flipped over" while going across the network and then flipped back when it reaches the other host. So all clients only ever see A.
That I know but I wasn't asking about DER-encoding. My query was for ECDSA signature.
Here's the steps for calculating ECDSA signature (wikipedia):
As you can see, z is taken as the L
n leftmost bits of 'e' where L
n is the bit length of the group order n. So, 'e' i.e. hash of message to be signed has to be in the specific order.