This seems to be a case for  a monoclonal  antibody : the strategy would be to get a library of monoclonals that react with your target protein and the to screen for those that don't cross-react with the related protein. But it will likely take hard work and some luck.

Pierre Beguin,

Thank you for the suggestion, but, my task is to generate the antigen by cloning the desired peptide into pET23d, express in bacteria using Terrific broth and purify the protein and use it as an antigen after adding appropriate hapten. I do not think I can go for monoclonal antibody now. So, can you please suggest in regard to my above-explained methodology?

You don't say what the overall identity/homology of your protein of interest has with the other protein but if there is a high degree of homology it will be very difficult/impossible to raise a polyclonal antibody that will be specific to your ptotein. If you can't  go for monoclonals, the alternative is to raise a polyclonal against you protein of interest and then make an affinity column with the other protein (immobilise the antigen on something like a HiTrap NHS-activated sepharose column) and try and absorb out the cross-reacting antibodies. I have done this successfully with two highly similar rat mast cell proteases, such that I was able to get dual immunofluorescence labeling on the same tissue section. This process is also a lot of work and will require the serum to be passed through the affinity column several times and there is no guarantee of success.

One way to deal with this problem is by "cascade immunisation"

1 Immunise a rabbit (or sheep...) with the interfering protein to get a good titre of IgG antibodies. Bleed this animal. you can then purify the IgG fraction if you wish

2 Immunise a second rabbit with your desired antigen. An hour or two after each injection give an injection of IgG from the first immunised animal. You should give a fairly large dose but it depends on the titre

The passively given  antibodies inhibit the immune response to the interfering protein and allows antibodies to be made to the unshared determinants.

This is a good technique and should work if there are unshared deteminants

Do you need antibody binding to the hapten or the protein? Maybe you could try panning some antibody library.

Without a more complete description of how these antibodies are to be used it is difficult to offer the best approach, and you could unnecessarily end up spending a lot of time trying to solve a difficult or intractable problem.   Please explain exactly how you plan to use the antibodies that you are seeking?   Could an immunogenic sequence be cloned into your short protein to permit unique recognition in the presence of the larger protein?  Must the antibody and anti-hapten antibody bind non-competitively?  Will there be one or multiple haptens per protein and will the larger protein also be haptenated? Chances are that there is a simpler way to solve your problem than the tedious process of raising specific polyclonal antibodies.