You can do this with a CASE statement.
Select Top 1000000 Case
When DatePart(Month, tblAssetCustom.Warrantydate) >= 10 Then
Cast(DatePart(Year, tblAssetCustom.Warrantydate) + 1 As nvarchar) + ' Q1'
When DatePart(Month, tblAssetCustom.Warrantydate) <
4 Then Cast(DatePart(Year, tblAssetCustom.Warrantydate) As nvarchar) + ' Q2'
When DatePart(Month, tblAssetCustom.Warrantydate) >= 4 And
DatePart(Month, tblAssetCustom.Warrantydate) < 7 Then Cast(DatePart(Year,
tblAssetCustom.Warrantydate) As nvarchar) + ' Q3'
When DatePart(Month, tblAssetCustom.Warrantydate) >= 7 And
DatePart(Month, tblAssetCustom.Warrantydate) < 10 Then Cast(DatePart(Year,
tblAssetCustom.Warrantydate) As nvarchar) + ' Q4'
End As [warranty expiration],
tblAssets.AssetID,
tblAssets.AssetName,
tsysAssetTypes.AssetTypename,
tsysAssetTypes.AssetTypeIcon10 As icon,
tblAssets.Lastseen
From tblAssets
Inner Join tblAssetCustom On tblAssets.AssetID = tblAssetCustom.AssetID
Inner Join tsysAssetTypes On tsysAssetTypes.AssetType = tblAssets.Assettype
Where tblAssetCustom.State = 1
Order By tblAssetCustom.Warrantydate