A pure fusion bomb would produce less fallout per unit yield than a fission only bomb but it would still produce some as others have noted fusion bombs contain a primary fission explosion that is required to set off the fusion reaction.
In the real world, most fusion bombs are actually fission-fusion-fission bombs where a primary fission explosion with fissile martials (U-235 or Pu-239) ignites a fusion reaction. The extremely high energy neutrons of the fusion reaction subsequently set off a tertiary U-238 tamper to an enormous fission explosion. Since U-238 is not fissile, you can put as much of it in the bomb as you want without a risk of it reaching critical mass.
The Tsar bomb (the largest manmade explosion ever) had a yield of 50 megatons of mostly fusion. But the original design had a U-238 tamper that would have increased the yield to over 100 megatons but would have produced an enormous amount of fallout. Before the test it was decided to remove the tamper to limit the fallout.
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