There are various govt institutes and private companies that will do the sequencing. For govt organizations or institutes you have to inquire in your area. I personally used agrigenome and eurofins for sequencing. Both of their quality of sequencing is good. I dont think anyone will do it for free unless you have strong recommendation.
Apart from the above suggestions, you can also go for Macrogen Korea (https://dna.macrogen.com/eng/). They provide very fast (2-3 working days) and high quality sequencing results.
If you have more than 20 reactions then your shipping cost will be covered by Macrogen.