wikipedia is a good introduction to autism.
SNPs or haplotypes that have been reported to be associated with autism include:
- A SNP in chromosomal region 5p15, rs10513025, for which the rarer allele is associated with reduced risk for autism, based on a large study of over 1,500 cases from over 1,000 families.10.1038/nature08490
- A deletion or duplication of a section of chromosome 16 appears to account for ~1% of de novo cases of autism. The 593kb region spans from ~29.5-30.1M on ch16. 10.1056/NEJMoa075974
- 3 studies implicate SNPs in the CNTNAP2 gene as increasing risk for autism; see rs7794745, rs2710102
- A microsatellite in the 'disrupted in schizophrenia' DISC1 gene is associated with autism, and a SNP rs1322784 and haplotype ("HEP3") are associated with asperger's syndrome [PMID 17579608]
- A haplotype in the brain-derived neurotrophic factor BDNF gene associated with autism [PMID 17349978]
- Haplotypes in the gene encoding protein kinase c-beta (PRKCB1) on chromosome 16 are associated with autism [PMID 16027742]
- A haplotype of the dopamine D1 receptor DRD1 gene associated with autism in families having only affected males; see rs265981, rs4532 and rs686.[PMID 18205172]
- A SNP (rs2745557) in the cyclooxygenase-2 (Cox-2) gene, reported to be overtransmitted in Korean families.[PMID 18579107]
- A SNP (rs1143674) in the integrin alpha-4 (ITGA4) gene, reported in Irish and American families [PMID 18846500]
- A SNP (rs2217262) in the dedicator of cytokinesis 4 (DOCK4) gene, which codes a protein involved in intracellular signalling was associated with a 2 to 4 times increased risk of Autism [PMID 19401682]
- Certain mtDNA haplogroups are reported to have higher autism incidence; "relative to the most common European haplogroup HHV, European haplogroups I, J, K, O-X, T, and U were associated with increased risk of ASD, as were Asian and Native American haplogroups A and M, with odds ratios ranging from 1.55 (95% CI, 1.16-2.06) to 2.18 (95% CI, 1.59-3) (adjusted P < .04)" [PMID 28832883]
Older fathers linked to autism 
Rett Syndrome, a form of autism
Researchers re-introduced a fully functional version of the MECP2 gene into mice that had been born with damaged MECP2 genes. Contrary to their expectations, the mice improved. In the article's words, 'restoration of fully functional MECP2 over a four week period eradicated tremors and normalized breathing, mobility and gait in mice that had previously been fully symptomatic and, in some cases, only days away from death.' The ramifications for people suffering from Rett Syndrome are obvious, but mutations of the MECP2 gene are also believed to be the cause of 'classic' autism, and a number of other neurological disorders."