<p>Is there a way to retrieve an article&#39;s citation index via Pubmed or Pubmed&#39;s eutils or any other way in Pubmed/Entrez? Or a way to filter the search results based on citation index in pubmed?</p>

If by "citation index" you mean the number of times a paper is cited, then not really. The closest you'll come is the number of citations indexed in Pubmed Central. Using R:

    library(rentrez)
    
    get_pmc_cites <- function(pmid){
        res <- entrez_link(db="pmc", dbfrom="pubmed", id=pmid)
        return(length(res$pubmed_pmc_refs))
     }
    get_pmc_cites(20203609)
    # [1] 25

***EDIT***

Just noticed the summary xmls for pubmed have the PMC reference count, which might make multiple calls quicker:

    recs <- entrez_summary(db="pubmed", id=c(20203609, 20203610))
    sapply(rec, "[[", "PmcRefCount")
    # [1] 25 200