select
b.MedioID
,a.[NoticiaID]
,a.[Pagina]
b.[FechaAlta]
FROM base1.[dbo].noticiaptest as a inner join (
select
[MedioID]
min([FechaAlta]) as FechaAlta
FROM base1.[dbo].noticiaptest
where [FechaAlta] > GETDATE()-1 and medioid in (349, 39558, 504, 1464, 1170, 566, 160, 478, 55162) and pagina =1
group by MedioID
) as b
ON a.MedioID = b.MedioID and a.FechaAlta = b.FechaAlta
order by lo que quieras