The currently assigned sort order determines the order in which results are returned.

You can change the sort order using the SortField field, which is available in XV1ConversationFilterInfo, XV1SocialObjectFilterInfo, and others. For example, this request returns results sorted by Conversation age, with the newest Conversation first:

/conversations?filter={"LimitToStarred":true,"ExcludeMuted":true,"SortField":CONVERSATION_IS_NEW}