I’m sorry. I thought you were talking about being a missionary abroad in in the American homeland missions. It sounds like what you’re looking for is for a ministry.
Do you have a Catholic Charities in your town or a diocesan ministry, such as a pro-life office? Some dioceses also have ministries to the disabled, elderly, immigrants and other special groups. These are at a diocesan level rather than a parish level. They may require that you travel across the county or to the neighboring county, but not outside the diocese. A lot depends on the diocese that you belong to. The bigger dioceses have more possibilities.
You can also link up with one of the religious communities involved in ministries to special populations. You may want to check to see if you have any Franciscans, Missionaries of Charity, Daughters of Charity, Jesuits, Missionhurst or other religious who engage in ministry to the poor. These are the usual communities that do this type of ministry. At least they are the larger ones. There are also smaller communities involved in special ministries.
Fraternally,
Br. JR, OSF