The real answer is, "Ask your DM", but at my table.
The new Haste (usually) overrides the old one.
The rules for combining effects of the same spell cast multiple times from the PHB:
The effects of the same spell cast multiple times don't combine, however. Instead, the most potent effect—such as the highest bonus—from those castings applies while their durations overlap.
They can't be under the effects of both Haste spells at once as the other answer suggests, and the clause...
When the spell ends, the target can’t move or take actions until after its next turn, as a wave of lethargy sweeps over it.
...is still an effect of the Haste spell.
I would apply the spells in order of highest spell level first, followed by longest remaining duration. Your mileage may vary depending on DM. See the question, How do you determine the 'most potent effect' for overlapping spells? for various methods of determining the potency of spell effects.
Exceptions I haven't considered almost certainly exist. But as a few hypotheticals, casting a second Haste spell after the first expires wouldn't be overlapping spells. If your wizard stops concentrating on the first Haste to cast a second one before it expires, your first one still "ends" and you suffer the consequences before the second one kicks in.
Or a higher level (or otherwise more "potent") Haste spell may prevent the new one from taking effect until the original ends.
Either of which creates a scenario like your third option.
See Will an Antimagic Field on a target of a "Haste" spell trigger the wave of lethargy? for another related exceptional hypothetical.