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SELECT 
  a.variant_id, 
  a.option_id, 
  a.position, 
  a.modifier, 
  a.modifier_type, 
  a.weight_modifier, 
  a.weight_modifier_type, 
  b.variant_name, 
  IF(
    shared_option_variants.variant_id IS NOT NULL, 
    shared_option_variants.modifier, 
    a.modifier
  ) as modifier, 
  IF(
    shared_option_variants.variant_id IS NOT NULL, 
    shared_option_variants.modifier_type, 
    a.modifier_type
  ) as modifier_type 
FROM 
  cscart_product_option_variants as a 
  LEFT JOIN cscart_product_option_variants_descriptions as b ON a.variant_id = b.variant_id 
  AND b.lang_code = 'en' 
  LEFT JOIN cscart_ult_product_option_variants shared_option_variants ON shared_option_variants.variant_id = a.variant_id 
  AND shared_option_variants.company_id = 1 
WHERE 
  a.option_id IN (340) 
  AND a.status = 'A' 
ORDER BY 
  a.position, 
  a.variant_id

Query time 0.00052

Explain
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	a	ref	status,option_id,option_id_2	option_id	6	const,const	9	Using index condition; Using where; Using filesort
1	SIMPLE	b	eq_ref	PRIMARY	PRIMARY	9	mahm3t_cs443.a.variant_id,const	1	Using where
1	SIMPLE	shared_option_variants	eq_ref	PRIMARY,company_id	PRIMARY	7	mahm3t_cs443.a.variant_id,const	1

Result

variant_id	option_id	modifier_type	weight_modifier_type	variant_name
7694	340	A	A	20 mm
7695	340	A	A	30 mm
7696	340	A	A	40 mm
7697	340	A	A	50 mm
7698	340	A	A	60 mm
7699	340	A	A	80 mm
7700	340	A	A	100 mm
7701	340	A	A	120 mm
7702	340	A	A	140 mm
7703	340	A	A	150 mm
7704	340	A	A	160 mm
7705	340	A	A	180 mm
7706	340	A	A	200 mm
7707	340	A	A	220 mm
7708	340	A	A	240 mm
7709	340	A	A	250 mm
7710	340	A	A	300 mm