CREATE TABLE [dbo].[test_ice] (
[id] int IDENTITY(1, 1) NOT NULL,
[id2] int NOT NULL)
ON [PRIMARY]
WITH (DATA_COMPRESSION = NONE);

CREATE UNIQUE NONCLUSTERED INDEX [ix_test_ice_id2_id]
ON [dbo].[test_ice]
([id2] , [id])
WITH
(
PAD_INDEX = OFF,
FILLFACTOR = 1,
IGNORE_DUP_KEY = OFF,
STATISTICS_NORECOMPUTE = OFF,
ALLOW_ROW_LOCKS = ON,
ALLOW_PAGE_LOCKS = ON,
DATA_COMPRESSION = NONE
)
ON [PRIMARY];
GO

select distinct t.id2, min(t.id) OVER(PARTITION BY id2) AS min_id
 from test_ice as t with (index (ix_test_ice_id2_id))

 select t.id2, min(t.id) OVER(PARTITION BY id2) AS min_id
 from test_ice as t with (index (ix_test_ice_id2_id))
 group by t.id2

Msg 8120, Level 16, State 1, Line 1
Column 'test_ice.id' is invalid in the select list because it is not contained in either an aggregate function or the GROUP BY clause.

 select t.id2, min(t.id) OVER(PARTITION BY id2) AS min_id
 from test_ice as t with (index (ix_test_ice_id2_id))
 group by t.id2, min(t.id) OVER(PARTITION BY id2)

Msg 4108, Level 15, State 1, Line 3
Windowed functions can only appear in the SELECT or ORDER BY clauses.

select t.id2, min(t.id)
from test_ice as t  with (index (ix_test_ice_id2_id))
group by t.id2