The ties were pulled out on TalkSPORT 2 tonight after many fell by the wayside this weekend.
Most teams have a round to negotiate, with the rearranged games taking place over the coming days.
The fourth round ties are due to take place over the weekend of Saturday 14 January 2023.
National League leaders Notts County have another home game to look forward to after beating Chorley.
Dorking Wanderers are through after defeating Yeovil Town and welcome Kidderminster Harriers.
Aldershot Town are at home to Leiston while Hungerford Town host Tamworth. They meet at Bulpit Lane in January.
Wrexham want to win the FA Trophy after going so close last year.
Scunthorpe stand in their way before the Dragons possibly head to Manchester to face Altrincham.
Third round winners receive £4,500 from the FA's prize pot.
Those who claim victory in January’s fourth round earn £5,250, with the losers taking home £1,500
The draw in full:
Gateshead vs Oldham Athletic
Dorking Wanderers vs Kidderminster Harriers
Notts County vs Maidstone United
Bracknell Town vs Bath City
Swindon Sup or Harrow vs FC Halifax Town
Dagenham & Red vs Maidenhead
Altrincham vs Wrexham or Scunthorpe
Solihull Moors vs Barnet
Torquay United vs Taunton Town
Southend United vs Darlington
Aldershot Town vs Leiston
Banbury United vs Coalville
Eastleigh vs Braintree Town
Hungerford Town vs Tamworth
York City vs Chelmsford or Wealdstone
Farsley Celtic vs Marske