In Cube, in the alarm console create a filter how you want it, and save it as a public alarm filter.

Via the WebAPI, you can use the GetAlarms method and specify this saved alarm filter:

{
    "connection": "862844db-4e3c-42f4-a6a2-a26764f05663",
    "filter": {
        "History": false,
        "SlidingWindow": false,
        "FilterItem": {
            "__type": "Skyline.DataMiner.Web.Common.v1.DMAAlarmFilterSavedFilter",
            "Filter": "sharedusersettings:My public alarm filter",
            "Match": true
        },
        "StartTime": 0,
        "EndTime": 0,
        "Masked": false,
        "InfoEvents": false,
        "Columns": [],
        "Limit": -1,
        "SortBy": null,
        "SortAscending": true
    }
}

Replace the connection string and replace "My public alarm filter" with the name of your public alarm filter. You can also enable History and specify a start/endtime.