You need to work at least partially with single stranded DNA, to favor annealing of both fragments. Either run two separate assymetric PCR reactions - one for A, the other for B, use much less concentration of "inner" -ie that one that should overlap with the other fragment)primer. Then mix aliquots of both PCR reactions and amplify using outer primers only (try several dilutions to see which works the best). The second option is to amplify both separate fragments with minimal concentration of primers, mix both PCR products 1:1, dilute (use a series of log dilutions - PCR product should be present in trace amount only). Use the diluted mixture as a template for PCR, that uses "outer" primers only (ie Fw from product A, rev for product B).

Will you please explain a bit about the asymmetric PCR reaction? Also, I'm following something similar to your second suggestion, but without any dilution. Will proceed with a series of diluted templates this time. Thank you so much.

Asymetric means, that concentration of one primer is markedly lower than usual. As a result, this primer will be used up during PCR. This will cause single-primer amplification of your product (ie product will be single-stranded). Single stranded product is needed for fusing overlapping fragments (double stranded typicly does not work, as reannealing of the original fragment is way more likely, tha annealing of fw strand of fragment A with rev strand of fragment B).