Does a stepchild qualify for adjustment of status?

You may file for your step son. For a step-child petition, the marriage between the child's biological parent and the US citizen step-parent must take place prior to the child's 18th birthday. You appear to satisfy that criteria, therefore, you may petition for him. Adjustment of status is most likely possible, provided he made a lawful entry. If he entered on the Visa Waiver Program and overstayed, you may encounter some difficulties in getting him adjusted. As always, it is best that you work with an attorney to ensure that the filing and supporting evidence are prepared correctly.

Because your step-son was below 18 years old when you married his mother, you can file an immediate relative petition for him. Therefore, he can adjust in the US just like what your wife did.

Based upon the facts you present it appears that you can petition for your step-son and he can adjust his status to that of a lawful permanent resident in the United States. Consult with an experienced immigration attorney for more information and specific advice on how best to proceed.