What's the role of SNP (Single Nucleotide Polymorphism) in a disease when there is no gene associated to that SNP
SNPs do not signify anything about the functionality of a particular piece of DNA. You can think of a SNP as just a sign that says &quot;hey, something in my neighborhood might be interesting!!&quot; In this respect many GWAS SNPs are so-called &quot;tag SNPs&quot;, that have been selected specifically to give the minimal number of SNPs that can be linked to all of the genome (e.g. every 1 centimorgan there is a SNP, or whatever).
So: SNPs do not say anything about biology, or about genes. The only thing that they signify is linkage to something that is possibly interesting.
Your issue seems to be that you are coming up with GWAS SNPs that do not show apparent linkage or statistical associations (e.g. eQTLs) to anything that you think should be interesting.
There are a lot of ways in which this could be the case:

There actually is a gene in that part of the sequence, and we just haven't annotated it properly.

The reference genome is wrong in that SNP's location, or is missing an interesting piece of sequence (i.e. a gene) that exists in your population.

That SNP has a population structure signal (i.e. it is more common in one population than another) that is associated with your trait of interest, which you have not properly corrected for.

That SNP is spuriously linked (for whatever reason) to a more distant part of the genome.

That SNP was mis-mapped and is actually in the wrong part of the genome somehow.

There is technical interference due to high similarity to some other part of the genome, which your procedure has not corrected for.

Sometimes frequentist p-values are not actually informative and a thing that looks interesting according to p-values is simply not interesting.

Though there are no genes, there is a long-range enhancer in the region of the SNP that affects a distant gene.

Though there are no genes, there is repetitive DNA linked to the SNP that leads to a complicated regulatory feedback that affects something about your character of interest.

Something about microRNAs?

Your SNP doesn't have any genes nearby, but it is linked to a TAD boundary that affects overall chromatin architecture.

There is a long non-coding RNA there.

Your eQTL significance threshold is too stringent.

Your eQTL association analysis missed an important isoform or transcript.


... and many other hypotheses! Many of these are very hand-wavey or unlikely, but sometimes biology is just weird.
However, in general I would default to an explanation in which there is some kind of technical or statistical artifact. Even when nothing is obviously wrong, there is usually some kind of technical problem in genomic datasets.