You say you "would like to proof that gene A binds to its target gene (B) by specific consensus sequence and affects specific regulation of gene B, such as..."

Let's be clear about what exactly you want to prove.

If your statement above is correct, then you want to study a "gene A-gene B interaction". To do that, the easiest approach is to do 3C-qPCR assay, where you can map intergenic contacts using a few primers from gene A and a few from gene B, in multiple combinations. You have to digest formaldehyde-crosslinked cells with a suitable restriction enzyme, ligate with T4 DNA ligase, extract DNA, and use the ligated DNA as the template for qPCR. Refer to a good 3C protocol (for example, https://www.nature.com/articles/nprot.2007.243).

But I doubt that is what you meant. I guess you meant to study (1) if the protein A (your RBP of interest) binds gene B and regulate its expression, or (2) if your RBP binds the gene B transcript, and affects its translation.

If your question is (1) above, then you first have to determine if your RBP is a sequence-specific DNA-binding protein. Look bioinformatically if it has any DNA-binding motifs/domains. Irrespective of whether it has DNA-binding motifs or domains, it can still associate with gene B (via its binding to a gene B-binding transcription factor). So, the best way forward is to ChIP-qPCR for this protein and look at various locations along gene B. If you find that it binds gene B, then you can overexpress and knockdown RPB and measure the expression of gene B.

If your question is (2), then you can to the following:

1. Immunoprecipitate RPB, and analyze the material by RT-qPCR using primers for gene B. That will tell you if gene B transcript binds your RPB or not.

2. Alternatively, generate gene B transcript by in vitro transcription, and co-incubate this RNA with recombinant RPB. You can measure the association in two ways. (i) Just as above, by RT-qPCR, if you use anti-RPB to pulldown the RPB-RNA complex, and (ii) by RPB western blotting if your RNA is biotinylated and you used streptavidin pulldown for the RPB-RNA complex.

Once you ascertain the RPB-gene B transcript binding, then you can overexpress or knockdown RPB and measure "protein level" of gene B product. That would hint at whether or not RPB impacts translation of gene B transcript. If it does, you can study further by ribosome profiling. More on that later, but first you need to do as described above.

But most importantly, ask yourself what your hypothesis is! It seems you are not clear about what you are asking!

Good luck.

If what you want to test is whether PROTEIN A binds RNA B, this guide might be useful:

https://www.thermofisher.com/us/en/home/life-science/protein-biology/protein-biology-learning-center/protein-biology-resource-library/pierce-protein-methods/methods-detecting-protein-rna-interactions.html

Briefly, these are: RNA-IP (the one you did already; probably best choice), EMSA and FISH assays.

You can also go for CLIP experiments (iClip, ParClip) if you want to get transcriptome-wide binding information.