If you want obtain a full-length sequences using overlap amplified method, I suggest you can directly add two fragment products together with primers in same system, then amplify 30 cycles. I think it will get what you want to. Just like what you said, there are some mutant sites in the amplified sequences, but I think that maybe just only a few mutant sites that can not affect amino acid coding.If you want to figure out this status, you can choose high fidelity DNA polymerase.

another method you can choose:

You can join this two fragments into the same vector using restriction endonuclease

Instead of the overlapping PCR protocol, it is wiser to use Phusion polymerase and amplify 1.8kb fragment in one go. 1.8kb should not be difficult to amplify.

If you want to continue with the overlapping PCR protocol, using Taq-amplified fragments is not a good idea, particularly, when dealing with ORF. This usually disrupts the reading frame.

Still, you have a rare chance. Carefully check the adjacent bases of the overlapping region. If there is a "T" and "A" at 5' and 3' end of the overlap region (see figure), respectively, then you can use these Taq-amplified fragments (check your luck).

If you are lucky, follow this protocol

1. Mix both the fragments in equal quantities (No. of copies) in 10uL PCR-grade water. Heat the mixture at 95 C for 5 min and allow it to cool gradually to room temperature (RT) by keeping the tube at RT for 10 min.

2. Add 10uL 2x PCR master mix (without primer and template) to the mixture prepared in step 1.

3. Incubate at 68 or 72 C for 10 min. The product of this reaction will have some full length (1.8kb) copies. Use this as a template in a fresh PCR reaction with f-1 and r-2 primers (see figure). Run up to 30-35 cycles.

If you are not lucky, amplify the fragments using Phusion polymerase and follow the above three steps.

@ shixing 

I have used the high fidelity polymerase like Deep Vent and Phusion. Both are not giving even a smear. Tried every possible annealing temperature which I got bands in GT Emerald and Taq Pol.

Restriction comes in the end part. The primer sequence itself is designed with the restriction sites in the first end and the last end to favor the cloning.

@Mohan, 

I have got two individual fragments from GT emerald , which I have subjected for  blunting using the T4 DNA polymerase, by incubating it @ 12oC for 15 minutes. As I have mentioned, high fidelity pols are not working for my condition. Normally we use Taq to standardise and then start playing with the annealing temperature around the same with high fidelity, right.. That is not working here.

Yes the Step I was talking about.

The mix without Primers and then several more cycles with primer. I have tried that, and got joined product. But the band with smear. I'm hereby attaching the Image of the Gel.  what I have noticed was, as the number of cycle and concentration of the template increases the smear level also increases.

@aliakbar,

I have tried that. All I can see was just the smear from the well till the run area.

Thank you very much everyone for your time and valuable suggestions. Really really appreciate you helping mentality.

I will update you all once get the joined one which is apt for cloning.