You would have to convert the field using the code below, similar to what you did with your custom field. Simply replace the highlighted code with the field which you want in the European date format.
Convert(nvarchar,tblAssetCustom.PurchaseDate,103) As Date
I left the custom field conversion as is, but you can change it to be the same by changing the code to 103.
Select Top 1000000 tsysAssetTypes.AssetTypeIcon10 As icon,
tblAssets.AssetID,
tblAssets.AssetName,
Convert(datetime,tblAssetCustom.Custom11,120) As Wartungsvertrag,
tblAssetCustom.Serialnumber,
Convert(nvarchar,tblAssetCustom.PurchaseDate,103) As [Purchase Date],
Convert(nvarchar,tblAssetCustom.Warrantydate,103) As [Warranty Expiration],
tsysAssetTypes.AssetTypename As Type,
tblAssets.IPAddress,
tblAssets.Description,
tblAssetCustom.Manufacturer,
tblAssetCustom.Model,
tblAssetCustom.Location,
tsysIPLocations.IPLocation,
tblAssets.Lastseen
From tblAssetCustom
Inner Join tblAssets On tblAssetCustom.AssetID = tblAssets.AssetID
Inner Join tsysAssetTypes On tsysAssetTypes.AssetType = tblAssets.Assettype
Left Join tsysIPLocations On tblAssets.LocationID = tsysIPLocations.LocationID
Where tblAssetCustom.Custom11 < GetDate() + 60 And tblAssetCustom.Custom11 >
GetDate() And tblAssetCustom.State = 1
Order By [Warranty Expiration] Desc