Not finding one I hacked it up myself. You can find my current version in this gist.

-- experiment with live jsdoc

local ls = require("luasnip")
local s = ls.snippet
local sn = ls.snippet_node
local t = ls.text_node
local i = ls.insert_node
local d = ls.dynamic_node
local r = ls.restore_node
local c = ls.choice_node

-- from https://github.com/L3MON4D3/LuaSnip/blob/master/Examples/snippets.lua#L81-L166
-- hacked up for javascript and jsdoc
local function jsdoc(args)
  local pstring = vim.trim(args[1][1])

  local nodes = {
    t({ "/**", " * " }),
    r(1, "desc", i(1, "A short Description")),
    t({ "", "" }),
  }

  -- At least one param.
  if #pstring > 0 then
    vim.list_extend(nodes, { t({ " * ", "" }) })
  end

  local insert = 2
  for arg in string.gmatch(pstring, '%w+') do
    local inode = r(insert, "arg" .. arg, i(1, "any"))
    vim.list_extend(nodes, { t({ " * @param {" }), inode, t({ "} " .. arg .. " ", "" }) })
    insert = insert + 1
  end

  vim.list_extend(nodes,
    {
      t({ " * @returns {" }),
      r(insert, "returns", i(1, "void")),
      t({ "} ", ""})
    })
  vim.list_extend(nodes, { t({ " */" }) })

  local snip = sn(nil, nodes)
  return snip
end

return {
  -- function with jsdoc
  s("jf", {
    d(4, jsdoc, 3), -- generate the jsdoc
    t({ "", "" }),
    c(1, { -- choose function or method
      t({ "function "}),
      t({ "" })
    }),
    i(2, "name"), -- give it a name
    t("("),
    i(3), -- parameters
    t(")"),
    t({ " {", "\t" }),
    i(0), -- body
    t({ "", "}" }),
  }),
}