If you are using shape file feature source. You need call GetFeaturesInsideBoundingBox() to get feature collection. Then loop the collection to filter the records by column value. Because for the shape file we use R-Tree index(ids file) to do the spatial query. it not support the SQL statement.
If you are using the database which already support the Sql spatial query. You could build your statement to do the querying.
Something like this.
var connectionString = @"Data Source=\\192.168.0.3\Internal Test Data\Sqlite\Mapping.sqlite";
var ne_road10m_linestring = new SqliteFeatureLayer(connectionString, "Segments", "geomID", "geom");
ne_road10m_linestring.Name = ne_road10m_linestring.TableName;
ne_road10m_linestring.WhereClause = $"WHERE ReplicationState = 1 and [Contain statement]";