Steve I found this:
From Mankau/Petrick, "Messerschmidt Bf 110, Me 210, Me 410. Die Messerschmitt-Zerstörer und ihre Konkurrenten", it seems that at first the DB601N production went to (or was scheduled for) the bomb-carrying Me 110C Zerstörer.
Timeline:
24.05.1940: GL announces that 1000 DB601N engines are to be produced until 01.01.1940.
31.05.1940: Of the 1000 engines, 350 engines have to be considered reserve engines. Thus, only the series production Me 109F can be equipped with the engine. An introduction into Me 110 production at a later date is to be considered.
07.06.1940: New program shows Me 109 and Me 110 equipped with DB601N.
12.07.1940: Generalstab decides that the existing DB601N engines are for now to be installed in the Me 110 exclusively.
19.07.1940: The currently available DB601N engines are required for conversion of the Me 110 in front-line operations. This means an end to further conversions of the Me 109 (of which so far, one group has been converted). The Me 109F series retains the DB601N engine. New-production Me 110 retain the DB601A as before.
26.07.1940: Generalstab opposes further conversions of Me 110 aircraft to DB601N engines except for the groups currently under conversion.
09.08.1940: For the conversion of a total of 3 groups of Me 110 and the already completed conversion of one group Me 109, a monthly total of 70 engines is required for 30 replacement aircraft Me 110, 10 replacement aircraft Me 109. An additional 30 engines are allocated for the reserve engine pool. As currently 280 engines are used in operations, this equates a 10 % reserve.
30.08.1940: It is requested from LC 3 to built a reserve of 45 engines (September), 35 (October), then 30 engines each month until a total of 180 engines is reached.
27.09.1940: Chef Generalstab decided to sustain 4 groups of Me 110 with N engines. 40 of DB601N engines are ear-marked for the reserve pool for these groups. The remaining engines are to go into the reserve pool (1/3) and into Me 109 (2/3).
18.10.1940: It is impossible at the time to convert more than the one existing Bf 109E group to DB601N, and it's not expected to be possible before 01.12.1940. Currently the DB601N engines go to: 1) new production Friedrichs, 2) new production Me 110 to sustain the existing four groups, 3) into 40 new production Emils to sustain the existing one group, 4) into the reserve engine pool for 1 - 3.
26.10.1940: Until the end of October, 1100 - 1200 DB601N engines were delivered. They are installed in the four existing Me 110 groups and the single existing Me 109 group, some reconnaissance aircraft of the Aufklärungsgruppe Ob. d. L., plus 130 reserve engine pool. The rest of the engines went into Me 109F and Me 110 production. The production of DB601N-engined Me 110s is to be channelled into night fighters, for which a constant strength of 120 is demanded.
06.11.1940: Generalstab requests more Me 109 with DB601N-engines. In order to free the required engines, the Generalstab accepts that two month's worth of Me 110 production are delivered with DB601A exclusively (November and December production). The engines thus freed are to go to 1) remaining Bf 109E production, 2) III./ZG 26 Erprb.Gr 210. II./ZG 26 and II./ZG 76 are given low priority or have to swap their engines for DB601A if required.
22.01.1941: The Leitender Chef-Ingenieur has considered the fuel situation and suggest to possibly convert the Me 110 to DB601A engines. The Generalstab lists the operational aircraft with DB601N engine by 01.01.1940 (I think this should be 01.01.41) as follows:
Me 109E-1: 16
Me 109E-3: 1
Me 109E-4: 59
Me 109E-6: 1
Me 109E-7: 34
Me 109E-8: 2
Me 109F-1: 5
Me 110C-1: 4
Me 110C-4: 40
Me 110C-5: 12
Me 110C-7: 14
Me 110D-0: 18
Me 110D-2: 20
Me 110D-3: 8
Me 110E-1: 176
Me 110E-2: 14
He 111P: 8
Do 215: 68