Please stop writing “day in age.” As in:
Everybody has a smartphone now. In this day in age you can’t work effectively without one.
The correct phrase is “day and age.” With the combined (although somewhat redundant) meaning of “in this day” and “in this age.” It’s generally accepted to mean something along the lines of “in the world we live in today.” The phrase is a bit overused, qualifying as a tired cliché by some measures…but at least it makes sense!
“Day in age” doesn’t make any sense:
In this day in age, nobody speaks like that anymore.
What does that mean? There’s a day in this age? There’s an age in this day? What? It doesn’t mean anything. Stop saying it!
Unlike some past “Dear Internets” topics, there’s no wiggle room on this one. It almost always gets corrected before it makes it into print: Google Ngrams reports a first use (in print) in 1972, and while it’s been increasing, it’s still very nonstandard. In 2008 (the last year with good data), “day and age” was used about 200 times more often. Out on the vast expanse of “teh Internets,” copyediting is a bit more lax; but “day and age” still outnumbers “day in age” by roughly 36 to 1.
I’m an open minded guy, Internets, willing to change my conclusion if someone can make their case that I’ve got it wrong. If you can convincingly explain to me why “day in age” is anything other than illiterate nonsense, I might be willing to change my mind. So far, no one has even come close. But don’t be afraid to keep trying! Sisyphus never got anywhere until he started pushing that rock. For this problem, if you apply his kind of energy to the task, you might just get his kind of results.
[For those scoring at home, some have suggested that day in age qualifies as an eggcorn. I don’t see how this is so, since an eggcorn usually has meaning to it, often a meaning similar to the original phrase. Day in age doesn’t have meaning, which would make it a simple malapropism.]