Unfortunately you cannot export the custom field search results as the Export button allows you to either:

1. Export out a tag(s) group

2. Export out all contacts

You can export out all data and then sort by the custom field column heading to see the results of your custom field search.

Another option is to use tags to tag each contact with the relevant custom field entry such as 'month' or 'year' or even team members name which would then allow you to run a tag search and export out just that tag group - please find a link below to further information on this:

Can I export out a tag group?