In C# it would be like this:
table
.GroupBy(row => row.SomeColumn)
.Select(group => group
.OrderBy(row => row.AnotherColumn)
.First()
)
Linq-To-Sql translates it to the following T-SQL code:
SELECT [t3].[AnotherColumn], [t3].[SomeColumn]
FROM (
SELECT [t0].[SomeColumn]
FROM [Table] AS [t0]
GROUP BY [t0].[SomeColumn]
) AS [t1]
OUTER APPLY (
SELECT TOP (1) [t2].[AnotherColumn], [t2].[SomeColumn]
FROM [Table] AS [t2]
WHERE (([t1].[SomeColumn] IS NULL) AND ([t2].[SomeColumn] IS NULL))
OR (([t1].[SomeColumn] IS NOT NULL) AND ([t2].[SomeColumn] IS NOT NULL)
AND ([t1].[SomeColumn] = [t2].[SomeColumn]))
ORDER BY [t2].[AnotherColumn]
) AS [t3]
ORDER BY [t3].[AnotherColumn]
But it is incompatible with MySQL.
I based my answer on the title of your post only, as I don't know C# and didn't understand the given query. But in MySQL I suggest you try subselects. First get a set of primary keys of interesting columns then select data from those rows:
SELECT somecolumn, anothercolumn
FROM sometable
WHERE id IN (
SELECT min(id)
FROM sometable
GROUP BY somecolumn
);