How can i show shortest path with ant-path-leaflet?

Firstly,you need to know the ant-path plugin is not used to search the shortest way for you,it just displays the path by latitude and longitude which is set by yourself.

If you want to display the the route,you need set more latitude and longitude.

Here is a working demo like below:

<div id="map"></div>

@section Scripts
{
    <link rel="stylesheet" href="https://unpkg.com/leaflet@1.6.0/dist/leaflet.css"
          integrity="sha512-xwE/Az9zrjBIphAcBb3F6JVqxf46+CDLwfLMHloNu6KEQCAWi6HcDUbeOfBIptF7tcCzusKFjFw2yuvEpDL9wQ=="
          crossorigin="" />
    <script src="https://unpkg.com/leaflet@1.6.0/dist/leaflet.js"
            integrity="sha512-gZwIG9x3wUXg2hdXF6+rVkLF/0Vi9U8D2Ntg4Ga5I5BZpVkVxlJWbSQtXPSiUTtC0TjtGOmxa1AJPuV0CPthew=="
            crossorigin=""></script>
    <script src="~/lib/leaflet-ant-path-bower-master/leaflet-ant-path-bower-master/dist/leaflet-ant-path.js"></script>

    <style>
        body {
            margin: 0px;
        }
        #heading {
            text-align: center;
            padding: 20px;
            background: #333;
            color: #CCC;
        }
        a {
            color: #3388ff;
        }
        #map {
            position: absolute;
            height: 100%;
            width: 100%;
            background-color: #333;
        }
        .leaflet-canvas-layer {
            opacity: 0.55;
        }
    </style>
    <script>
        var map = L.map('map', {
            center:[44.057039, 12.551160],
            zoom: 11,
            maxzoom: 18,
            minzoom: 1,
            zoomControl: false,  
            editable: true, 
        });   
       L.tileLayer('http://{s}.tile.osm.org/{z}/{x}/{y}.png', {
                    attribution: '&copy; <a href="http://osm.org/copyright">OpenStreetMap</a> contributors'
            }).addTo(map);

        //add more latitude and longitude
        let arrs = [
        [44.0567000, 12.5552968],
        [44.056880, 12.555297],
        [44.056955,12.553081],
        [44.057004, 12.551313],
        [44.057039, 12.551160],
        [44.056712, 12.547406],
        [44.056737, 12.547216],
        [44.0567000, 12.5460868]
                ];
    var antPath = L.polyline.antPath;
    var path = antPath(arrs, {
        "paused": false,   　　
        "reverse": false,　　
        "delay": 3000,　　　　
        "dashArray": [10, 20],　
        "weight": 5,　　　　
        "opacity": 0.5,　　
        "color": "#0000FF",　
        "pulseColor": "#FFFFFF"　　
    });
    path.addTo(map);
    </script>               
}

Result: